Multiple choice

If the sum of the squares of roots of the equation ${ x }^{ 2 }+2x-P=0$ is $10$, then the value of $P$ will be

  1. $-3$
  2. $3$
  3. $6$
  4. $-6$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Roots alpha, beta. alpha+beta = -2, alpha*beta = -P. alpha^2 + beta^2 = (alpha+beta)^2 - 2*alpha*beta = (-2)^2 - 2(-P) = 4 + 2P. Given 4 + 2P = 10, so 2P = 6, P = 3.

AI explanation

Let the roots be alpha and beta. Using the sum and product of roots formulas for x^2 + 2x - P = 0, we get alpha + beta = -2 and alpha*beta = -P. The given condition states alpha^2 + beta^2 = 10, which can be rewritten using the identity (alpha + beta)^2 - 2*alpha*beta. Substituting the values gives (-2)^2 - 2(-P) = 10, which simplifies to 4 + 2P = 10. Solving this yields P = 3.

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