Quiz On Quadratic Equations For Class 10 Chapter 4

1. The factorization of 14a + 7b is ___

2(7a + 3b)

7a(2 + b)

7(2a + b)

14(a + b)

The given expression, 14a + 7b, can be factorized by taking out the common factor of 7. This leaves us with 7(2a + b), which is the correct answer.

Explanation

The given expression, 14a + 7b, can be factorized by taking out the common factor of 7. This leaves us with 7(2a + b), which is the correct answer.

2. Find the product of (4a + 3) (4a - 3) : ___.

12a2 - 9

8a2 + 9

16a2 - 9

16a2 + 2a - 9

The given expression is a product of two binomials. To find the product, we can use the formula for the difference of squares, which states that (a + b)(a - b) = a^2 - b^2. In this case, a = 4a and b = 3. Substituting these values into the formula, we get (4a + 3)(4a - 3) = (4a)^2 - 3^2 = 16a^2 - 9. Therefore, the correct answer is 16a^2 - 9.

Explanation

The given expression is a product of two binomials. To find the product, we can use the formula for the difference of squares, which states that (a + b)(a - b) = a^2 - b^2. In this case, a = 4a and b = 3. Substituting these values into the formula, we get (4a + 3)(4a - 3) = (4a)^2 - 3^2 = 16a^2 - 9. Therefore, the correct answer is 16a^2 - 9.

3. The indicated sum of y/3 + 5y/3 - 4y/3 is _________>

Y

2y/3

Y/3

10y/3

The indicated sum of y/3 + 5y/3 - 4y/3 simplifies to (1/3)y + (5/3)y - (4/3)y, which can be further simplified to (6/3)y - (4/3)y. Combining like terms, we get (2/3)y, which is equivalent to 2y/3.

Explanation

The indicated sum of y/3 + 5y/3 - 4y/3 simplifies to (1/3)y + (5/3)y - (4/3)y, which can be further simplified to (6/3)y - (4/3)y. Combining like terms, we get (2/3)y, which is equivalent to 2y/3.

4. Find the trinomial product of (4x + 3) (-2x - 5) : ___.

12x2 - 26x + 15

-8x2 + 14x - 15

-8x2 - 26x - 15

6x2 - 14x - 15

The given trinomial product can be found by multiplying the first terms of both binomials (4x and -2x), then multiplying the outer terms (-5 and 4x), and finally multiplying the last terms (3 and -5). The sum of these three products gives us the trinomial product. In this case, the trinomial product is -8x^2 - 26x - 15.

Explanation

The given trinomial product can be found by multiplying the first terms of both binomials (4x and -2x), then multiplying the outer terms (-5 and 4x), and finally multiplying the last terms (3 and -5). The sum of these three products gives us the trinomial product. In this case, the trinomial product is -8x^2 - 26x - 15.

5.

A

B

C

D

not-available-via-ai

Explanation

not-available-via-ai

6. Factor 81n² - 100 : ___.

(9n - 10)2

(81n + 10) (n - 10)

(9n - 10) (9n + 10)

(9n + 10)2

The given expression can be factored using the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b). In this case, a = 9n and b = 10. Therefore, the expression can be factored as (9n - 10)(9n + 10).

Explanation

The given expression can be factored using the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b). In this case, a = 9n and b = 10. Therefore, the expression can be factored as (9n - 10)(9n + 10).

7. A person purchased 5k + 2 items for a total cost of 35k2 + 29k + 6. The average cost per item was ___.

6k + 2

6k + 3

7k + 2

7k + 3

The person purchased 5k + 2 items for a total cost of 35k2 + 29k + 6. To find the average cost per item, we divide the total cost by the number of items. Therefore, the average cost per item is (35k2 + 29k + 6)/(5k + 2). Simplifying this expression, we get 7k + 3.

Explanation

The person purchased 5k + 2 items for a total cost of 35k2 + 29k + 6. To find the average cost per item, we divide the total cost by the number of items. Therefore, the average cost per item is (35k2 + 29k + 6)/(5k + 2). Simplifying this expression, we get 7k + 3.

8. The binomial factors of 2x² + 7x + 3 are ___.

(x + 3) (2x + 1)

(2x + 3) (x + 1)

(x + 3) (2x - 1)

(2x - 1) (x - 3)

The given expression is a quadratic trinomial. To factorize it, we need to find two binomial factors that when multiplied together, give us the original expression. The correct answer, (x + 3) (2x + 1), is obtained by factoring the trinomial using the distributive property.

Explanation

The given expression is a quadratic trinomial. To factorize it, we need to find two binomial factors that when multiplied together, give us the original expression. The correct answer, (x + 3) (2x + 1), is obtained by factoring the trinomial using the distributive property.

9. The indicated quotient of ( - 1/3xy) ÷ (-3xy) is ____________.

1/3

1

- 1/9xy

1/ 9x2y2

The given expression is a quotient of two negative terms, (-1/3xy) and (-3xy). When dividing negative terms, the negative signs cancel out, resulting in a positive quotient. The expression simplifies to 1/3xy divided by 3xy, which can be further simplified to 1/9x^2y^2. Therefore, the correct answer is 1/9x^2y^2.

Explanation

The given expression is a quotient of two negative terms, (-1/3xy) and (-3xy). When dividing negative terms, the negative signs cancel out, resulting in a positive quotient. The expression simplifies to 1/3xy divided by 3xy, which can be further simplified to 1/9x^2y^2. Therefore, the correct answer is 1/9x^2y^2.

10. The greatest common factor of x⁵y and x⁴ y² is ___.

X5y2

X4y

Xy

X2y

.

Explanation

.

11. The formula for area is A = lw. If a rectangle has an area of 2x2 + x - 3, its dimensions are ___.

L: 2x - 1 w: x + 3

L: 2x - 3 w: x + 1

L: 2x + 1 w: x - 3

L: 2x + 3 w: x - 1

The correct dimensions of the rectangle are l: 2x + 3 and w: x - 1. This can be determined by substituting these values into the formula for area, A = lw, and simplifying.

Explanation

The correct dimensions of the rectangle are l: 2x + 3 and w: x - 1. This can be determined by substituting these values into the formula for area, A = lw, and simplifying.

12.

A

B

C

D

The inequality 1 < |k| < 5 means that the absolute value of k is greater than 1 and less than 5. This includes both positive and negative values. Therefore, the integers that satisfy this inequality are:

-4, -3, -2

2, 3, 4

Graph A correctly represents these integers on the number line.

Explanation

The inequality 1 < |k| < 5 means that the absolute value of k is greater than 1 and less than 5. This includes both positive and negative values. Therefore, the integers that satisfy this inequality are:

-4, -3, -2

2, 3, 4

Graph A correctly represents these integers on the number line.

13. The excluded value(s) for y² + y + 5 / y + 4 is (are) ___.

Y = -4

Y = 4

Y = 0 ; y = -1

Y = 5 and y = 1

The excluded value for y in the expression y^2 + y + 5 / y + 4 is y = -4. This is because when y = -4, the denominator of the expression becomes 0, which is undefined. Therefore, y = -4 is excluded from the possible values for y in this expression.

Explanation

The excluded value for y in the expression y^2 + y + 5 / y + 4 is y = -4. This is because when y = -4, the denominator of the expression becomes 0, which is undefined. Therefore, y = -4 is excluded from the possible values for y in this expression.

14. The factors of 16y³ + 68y² + 42y are ___.

2(4y + 7) (2y + 3)

(4y2 + 14y) (4y + 3)

4y(2y + 5) (2y + 2)

2y(2y + 7) (4y + 3)

The given expression can be factored as 2y(2y + 7) (4y + 3). This can be found by looking for common factors and using the distributive property to simplify the expression.

Explanation

The given expression can be factored as 2y(2y + 7) (4y + 3). This can be found by looking for common factors and using the distributive property to simplify the expression.

15. The factors of 2 - 98n² are ___.

-2(7n - 1) (7n + 1)

2(1 - 7n) (1 + 7n)

2(7n - 1)2

-2(49n2 - 1)

The given expression can be factored as -2(7n - 1) (7n + 1). This can be determined by applying the distributive property and factoring out the common factor of -2 from each term.

Explanation

The given expression can be factored as -2(7n - 1) (7n + 1). This can be determined by applying the distributive property and factoring out the common factor of -2 from each term.