If-are-the-roots-of-ax-2-bx-c-0-then-find-the-quadratic-equation-whose-roots-are-

Question Number 26888 by Roshan last updated on 31/Dec/17

If α, β are the roots of {a x}^{2} + b x + c = 0

then find the quadratic equation

whose roots are α + β, α β .

Answered by Rasheed.Sindhi last updated on 31/Dec/17

{a x}^{2} + b x + c = 0

α + β = - \frac{b}{a}, α β = \frac{c}{a}

In required equation :

Sum of the roots = (α + β) + α β

= - \frac{b}{a} + \frac{c}{a} = \frac{c - b}{a}

product of the roots = (α + β) (α β)

= (- \frac{b}{a}) (\frac{c}{a}) = - \frac{b c}{a^{2}}

x^{2} - (Sum of roots) + (Product of roots) = 0

x^{2} - (\frac{c - b}{a}) x + (- \frac{b c}{a^{2}}) = 0

a^{2} x^{2} + a (b - c) x - b c = 0