If - - are the roots of ax2-bx-c-0 then -2 - -2 - - - is equal to

The correct option is B ac bc/a^2 α, β are the roots of nbsp; ax^2+bx+c=0 ⇒α + β = b/a, αβ = c/a αβ^2+α^2 β+αβ = αβ (α + β) + αβ ...

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Byju's Answer

Standard XII

Mathematics

Inverse of a Function

If α, β are...

Question

If $α, β$ are the roots of $a x^{2} + b x + c = 0$ then $(α β^{2} + α^{2} β + α β)$ is equal to

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

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

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

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Solution

The correct option is B $\frac{a c - b c}{a^{2}}$
$α, β$ are the roots of
$a x^{2} + b x + c = 0$
$\Rightarrow α + β = - \frac{b}{a}, α β = \frac{c}{a}$
$α β^{2} + α^{2} β + α β = α β (α + β) + α β$
$= \frac{c}{a} (- \frac{b}{a}) + \frac{c}{a} = \frac{a c - b c}{a^{2}}$

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If α,β are the roots of ax2+bx+c=0 then (αβ2+α2β+αβ) is equal to

The correct option is B ac−bca2α,β are the roots of ax2+bx+c=0⇒α+β=−ba,αβ=caαβ2+α2β+αβ=αβ(α+β)+αβ=ca(−ba)+ca=ac−bca2

If $α, β$ are the roots of $a x^{2} + b x + c = 0$ then $(α β^{2} + α^{2} β + α β)$ is equal to

The correct option is B $\frac{a c - b c}{a^{2}}$
$α, β$ are the roots of
$a x^{2} + b x + c = 0$
$\Rightarrow α + β = - \frac{b}{a}, α β = \frac{c}{a}$
$α β^{2} + α^{2} β + α β = α β (α + β) + α β$
$= \frac{c}{a} (- \frac{b}{a}) + \frac{c}{a} = \frac{a c - b c}{a^{2}}$