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29 March, 09:54

22. Which equation has solutions of - 2 and 3?

A. y=x²+x-6

B. y=x²-x-6

C. y = x + 5x + 6

D. y = x2-5x+6

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Answers (1)
  1. 29 March, 10:51
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    B. y=x²-x-6

    Step-by-step explanation:

    Consider the product ...

    0 = (x - a) (x - b) = x² - (a+b) x + ab

    This equation has solutions x=a and x=b. You will note that ...

    the constant is the product of the solutions (ab) the coefficient of x is the opposite of their sum ( - (a+b))

    For solutions of - 2 and 3, the constant will be (-2) (3) = - 6. This eliminates choices C and D.

    The sum of the solutions is - 2+3 = 1, so the coefficient of x is - 1, matching choice B.
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