Multiple choice

If $\displaystyle \alpha $ and $\displaystyle \beta $ are the roots of the equation $\displaystyle 2x^{2}-3x-6= 0$, then the equation whose roots are $\displaystyle \alpha ^{2}+2, \beta ^{2}+2$, is

  1. $\displaystyle 4x^{2}+49 x+118= 0.$
  2. $\displaystyle 4x^{2}-49 x+118= 0.$
  3. $\displaystyle 4x^{2}-49 x-118= 0.$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

For 2x^2 - 3x - 6 = 0, Vieta's formulas give the sum of roots alpha + beta = 3/2 and the product alpha*beta = -3. The sum of the new roots is (alpha^2 + 2) + (beta^2 + 2) = alpha^2 + beta^2 + 4 = ((alpha+beta)^2 - 2*alpha*beta) + 4 = ((3/2)^2 - 2*(-3)) + 4 = 9/4 + 6 + 4 = 49/4. The product of the new roots is (alpha^2 + 2)(beta^2 + 2) = (alpha*beta)^2 + 2(alpha^2 + beta^2) + 4 = (-3)^2 + 2(33/4) + 4 = 9 + 33/2 + 4 = 59/2. The required equation is x^2 - (49/4)x + 59/2 = 0, which simplifies to 4x^2 - 49x + 118 = 0.

Keep practicing — related questions