Multiple choice

Form the quadratic equation if its roots are: $\displaystyle\,-2$ and $\cfrac{11}{2}$

  1. $2x^2\,+\,7x\,-\,22\,=\,0$
  2. $2x^2\,-\,7x\,-\,9\,=\,0$
  3. $2x^2\,-\,7x\,-\,22\,=\,0$
  4. $2x^2\,-\,7x\,-\,11\,=\,0$
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C Correct answer
Explanation

If roots are r1 and r2, the equation is x^2 - (r1+r2)x + (r1*r2) = 0. Here, r1 = -2 and r2 = 11/2. Sum = -2 + 5.5 = 3.5 = 7/2. Product = -2 * 11/2 = -11. Equation: x^2 - (7/2)x - 11 = 0, which multiplies to 2x^2 - 7x - 22 = 0.

AI explanation

The sum of the roots is -2 + 11/2 = 7/2, and the product of the roots is -2 times 11/2 = -11. The required equation is given by x^2 - (sum)x + (product) = 0, so we have x^2 - (7/2)x - 11 = 0. Multiplying the entire equation by 2 to clear the fraction results in 2x^2 - 7x - 22 = 0.

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