Multiple choice

If the roots of a quadratic equation are $25$ and $-2$, then find the equation?

  1. $x^2-27x-50=0$
  2. $x^2-23x-50=0$
  3. $x^2-23x+50=0$
  4. $x^2+23x-50=0$
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B Correct answer
Explanation

If roots are 25 and -2, the equation is (x - 25)(x + 2) = 0. Expanding this: x^2 + 2x - 25x - 50 = 0, which is x^2 - 23x - 50 = 0.

AI explanation

For a quadratic equation with roots 25 and -2, the sum of the roots is 25 + (-2) = 23 and the product of the roots is (25)(-2) = -50. The required equation is x^2 - (sum of roots)x + (product of roots) = 0. Substituting the values gives the equation x^2 - 23x - 50 = 0.

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