Multiple choice

The quadratic equation with sum of roots $-1$ and product of roots $2$

  1. $x^{2}+x+2=0$
  2. $x^{2}+8x+16=0$
  3. $x^{2}+16x+8=0$
  4. $x^{2}+4x+5=0$
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A Correct answer
Explanation

A quadratic equation with roots sum S and product P is x^2 - Sx + P = 0. Here S = -1, P = 2. So x^2 - (-1)x + 2 = 0, which is x^2 + x + 2 = 0.

AI explanation

Using the formula for forming a quadratic equation from its roots, the required equation is x squared minus (sum of roots)x plus (product of roots) equals 0. Substituting the sum as -1 and the product as 2 gives x squared plus x plus 2 equals 0. The result is x squared plus x plus 2 equals 0.

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