Multiple choice

Form the quadratic equation if its roots are: $-3$ and $-11$

  1. $x^2\,-\,14x\,+\,33\,=\,0$
  2. $x^2\,+\,14x\,+\,33\,=\,0$
  3. $x^2\,+\,14x\,-\,33\,=\,0$
  4. $x^2\,+\,14x\,+\,18\,=\,0$
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B Correct answer
Explanation

A quadratic equation with roots r1 and r2 is x^2 - (r1+r2)x + (r1*r2) = 0. Here, r1+r2 = -3 + -11 = -14 and r1*r2 = 33. The equation is x^2 - (-14)x + 33 = 0, which is x^2 + 14x + 33 = 0.

AI explanation

The sum of the roots is -3 + -11 = -14, and the product of the roots is -3 times -11 = 33. Substituting these into the standard form x^2 - (sum)x + (product) = 0 yields x^2 - (-14)x + 33 = 0. Therefore, the required equation is x^2 + 14x + 33 = 0.

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