You visited us 1 times! Enjoying our articles? Unlock Full Access!

Sum and Product of Roots of a Quadratic Equation

Let α,β be ...

Question

Let $α, β$ be two roots of the quadratic equation $a x^{2} + b x + c = 0$ then find the value of $α^{2} + β^{2}$ .

Open in App

Solution

Given $α, β$ be two roots of the quadratic equation $a x^{2} + b x + c = 0$ .

Then from the relation between the roots and co-efficients we get,

$α + β = - \frac{b}{a}$ .....(1) and

$α . β = \frac{c}{a}$ .....(2).

Now,

$α^{2} + β^{2}$

$= (α + β)^{2} - 2 α . β$

$= \frac{b^{2}}{a^{2}} - 2 \times \frac{c}{a}$ [ Using (1) and (2)]

$= \frac{b^{2} - 2 a c}{a^{2}}$

Suggest Corrections

Similar questions

α, β

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

\frac{1}{α^{2}} + \frac{1}{β^{2}}

α, β

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

\frac{1}{α^{2}} + \frac{1}{β^{2}}

α, β

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

\frac{α^{2}}{β} + \frac{β^{2}}{α} =

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

α & β

\frac{1}{α^{2}} + \frac{1}{β^{2}}

a x^{2} +

+ c = 0

Δ = b^{2} - 4 a c

α + β, α^{2} + {β^{2}, α}^{3} + β^{3}

α, β

a x^{2} +

+ c = 0

Join BYJU'S Learning Program