Multiple choice

If a, b are the two roots of a quadratic equation such that $a+b=24$ and $a-b=8$, then the quadratic equation having a and b as its roots is:

  1. $x^{2}+2x+8=0$
  2. $x^{2}-4x+8=0$
  3. $x^{2}-24x+128=0$
  4. $2x^{2}+8x+9=0$
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C Correct answer
Explanation

a + b = 24, a - b = 8. Adding gives 2a = 32, so a = 16. Subtracting gives 2b = 16, so b = 8. The equation is x^2 - (a+b)x + ab = 0, which is x^2 - 24x + 128 = 0.

AI explanation

By adding the equations a + b = 24 and a - b = 8, we get 2a = 32, so a = 16. Substituting a into the first equation gives b = 8. Using the formula x^2 - (sum of roots)x + (product of roots) = 0, the equation becomes x^2 - 24x + (16 * 8) = 0, which simplifies to x^2 - 24x + 128 = 0.

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