Test- Ecuatia De Gradul Al Doilea

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| By Lili.ana9
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Lili.ana9
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Quizzes Created: 1 | Total Attempts: 226
Questions: 10 | Attempts: 226

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Test- Ecuatia De Gradul Al Doilea - Quiz

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Questions and Answers
  • 1. 

    Solutiile ecuatiei 2x2+3x+1=0 sunt -1 si -1/2:

    • A.

      Adevarat

    • B.

      Fals

    Correct Answer
    A. Adevarat
    Explanation
    The statement is true because when we substitute -1 and -1/2 into the equation 2x^2 + 3x + 1 = 0, we get a true statement. This means that both -1 and -1/2 are solutions to the equation.

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  • 2. 

    Descompunerea in factori a trinomului 6x2-5x-1=0 este:

    • A.

      (2x-1)(3x+1)

    • B.

      (6x+1)(x-1)

    • C.

      6(x-1)(x+1/6)

    • D.

      (6x-1)(x+1)

    Correct Answer(s)
    B. (6x+1)(x-1)
    C. 6(x-1)(x+1/6)
    Explanation
    The correct answer is (6x+1)(x-1). This is the correct factorization of the given trinomial 6x2-5x-1=0. The factors are (6x+1) and (x-1). The other option, 6(x-1)(x+1/6), is not a correct factorization of the trinomial.

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  • 3. 

    Ecuatia de gradul al doilea care are radacinile 4 si -3 este:

    • A.

      X2+x-12=0

    • B.

      X2-x-12=0

    • C.

      -x2-x+12=0

    • D.

      -x2+x+12=0

    Correct Answer(s)
    B. X2-x-12=0
    D. -x2+x+12=0
    Explanation
    The equation of the second degree that has the roots 4 and -3 can be found using the fact that the sum of the roots is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term, and the product of the roots is equal to the constant term divided by the coefficient of the quadratic term. By applying these formulas, we can determine that the correct equation is x2-x-12=0. The other option, -x2+x+12=0, does not satisfy these conditions.

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  • 4. 

    -5 e solutie a ecuatiei 3x2+2x-1=0

    • A.

      Da

    • B.

      Nu

    Correct Answer
    B. Nu
  • 5. 

    Daca discriminantul ecuatiei este zero, atunci ecuatia nu are solutii:

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    If the discriminant of the equation is zero, it means that the equation has one solution. This is because the discriminant is calculated as b^2 - 4ac, where a, b, and c are the coefficients of the equation. If the discriminant is zero, it indicates that the quadratic equation has a double root, which means that it has only one solution. Therefore, the correct answer is False.

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  • 6. 

    Daca (x-a)(2x+7)=2x2+x-21, atunci valoarea lui a este:

    • A.

      5

    • B.

      -3

    • C.

      3

    • D.

      -5

    Correct Answer
    C. 3
    Explanation
    To find the value of "a" in the equation (x-a)(2x+7)=2x^2+x-21, we need to expand the left side of the equation and then compare the coefficients of the like terms. Expanding the equation gives us 2x^2 + 7x - 2ax - 7a. Comparing the coefficients of x^2, x, and the constant term on both sides of the equation, we get 2 = 2 (coefficient of x^2), 1 = -2a (coefficient of x), and -21 = -7a (constant term). Solving these equations simultaneously, we find that a = 3.

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  • 7. 

    Daca x1 si x2 sunt radacinile ecuatiei ax2+bx+c=0, atunci x1+ x2 este:

    • A.

      -b/a

    • B.

      B/a

    • C.

      -c/a

    • D.

      C/a

    Correct Answer
    A. -b/a
    Explanation
    If x1 and x2 are the roots of the equation ax2+bx+c=0, then x1+x2 is equal to -b/a. This can be derived from the fact that the sum of the roots of a quadratic equation is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term. In this case, the linear term is b and the quadratic term is a, so the sum of the roots is -b/a.

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  • 8. 

    Daca x1 si x2 sunt radacinile ecuatiei ax2+bx+c=0, atunci x1x2 este:

    • A.

      -c/a

    • B.

      -b/a

    • C.

      B/a

    • D.

      C/a

    Correct Answer
    D. C/a
    Explanation
    If x1 and x2 are the roots of the equation ax2+bx+c=0, then x1x2 can be found by multiplying the roots together. In this case, x1x2 is equal to c/a.

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  • 9. 

    Daca discriminantul ecuatiei este negativ, atunci ecuatia are o solutie dubla:

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    If the discriminant of an equation is negative, it means that the equation does not have any real solutions. Therefore, it cannot have a double solution. Hence, the statement "ecuatia are o solutie dubla" (the equation has a double solution) is false.

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  • Current Version
  • Mar 20, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Mar 15, 2020
    Quiz Created by
    Lili.ana9
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