InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Let `f(x), g(x)`, and `h(x)` be the quadratic polynomials having positive leading coefficients and real and distinct roots. If each pair of them has a common root, then find the roots of `f(x) + g(x) + h(x) = 0`. |
|
Answer» Let `f(x) = a_(1) (x - alpha) (x - beta),` ` g(x) = a_(2) )x - beta) (x - gamma),` and `h (x) = a_(3)(x - gamma) (x - alpha),` where `a_(1), a_(2), a_(3)` are positive. Let `f(x) + g(x) + h(x) = F(x)` `rArr F(alpha) = a_(2)(alpha - beta)(alpha - gamma)` `F(beta) = a_(3) (beta - gamma)(beta - alpha)` `f(gamma) = a_(1) (gamma - alpha)(gamma - beta)` `rArr F(alpha) F (beta) F(gamma) = - a_(1) a_(2) a _(3) (alpha - beta)^(2) (beta - gamma)^(2) (gamma - alpha )^(2) lt 0 ` So, roots of `F(x) = 0 are and distinct. |
|