Multiple choice

Form the quadratic equation whose roots are: $-3$ and $\displaystyle \frac{5}{2}$

  1. $2x^{2}\, +\, x\, -\, 15\, =\, 0$
  2. $2x^{2}\, -\, x\, -\, 15\, =\, 0$
  3. $x^{2}\, +\, x\, -\, 45\, =\, 0$
  4. $x^{2}\, -\, x\, -\, 45\, =\, 0$
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A Correct answer
Explanation

A quadratic equation with roots r1 and r2 is given by x^2 - (r1 + r2)x + (r1 * r2) = 0. Here, r1 = -3 and r2 = 5/2. The sum is -3 + 2.5 = -0.5, and the product is -3 * 2.5 = -7.5. The equation is x^2 + 0.5x - 7.5 = 0. Multiplying by 2 gives 2x^2 + x - 15 = 0.

AI explanation

The sum of the roots is (-3) + (5/2) = -1/2 and the product of the roots is (-3) * (5/2) = -15/2. The required quadratic equation is x^2 - (sum)x + (product) = 0, yielding x^2 - (-1/2)x + (-15/2) = 0. Multiplying the entire equation by 2 gives 2x^2 + x - 15 = 0.

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