2018 · Q50
If a, p and y are the zeros of the polynomial i(x) = ax³ + bx² + cx + d, then α² + β² + γ² is equal to
Elementary MathematicsAlgebra
- Ab2−aca2/{b^2-ac}{a^2}
- Bb2−2aca/{b^2-2ac}{a}
- Cb2+2aca/{b^2+2ac}{a}
- Db2−2aca2/{b^2-2ac}{a^2}
Explanation
For ax^3 + bx^2 + cx + d: alpha + beta + gamma = -b/a and alpha*beta + beta*gamma + gamma*alpha = c/a. Then alpha^2 + beta^2 + gamma^2 = (alpha + beta + gamma)^2 - 2(alpha*beta + beta*gamma + gamma*alpha) = b^2/a^2 - 2c/a = (b^2 - 2ac)/a^2. Hence option D.