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

The correct option is A b^2 + 3ac/a^2 α , β are roots of the equation ax^2 bx c = 0 ⇒α+β=ba and αβ= ca α^2 αβ+β^2=(α+β ...

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Standard XII

Physics

Dimensional Analysis

If α, β a...

Question

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

\frac{b^{2} + 3 a c}{a^{2}}

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\frac{b^{2} - 3 a c}{a^{2}}

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

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

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Solution

The correct option is A $\frac{b^{2} + 3 a c}{a^{2}}$
$α$ , $β$ are roots of the equation $a x^{2} - b x - c = 0$
$\Rightarrow α + β = \frac{b}{a}$ and $α β = \frac{- c}{a}$
$α^{2} - α β + β^{2} = (α + β)^{2} - 3 α β$
$= {(\frac{b}{a})}^{2} - 3 (\frac{- c}{a})$
$= \frac{b^{2} + 3 a c}{a^{2}}$
Hence, option A.

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If α, β are roots of the equation ax2−bx−c=0, then α2−αβ+β2 is equal to

The correct option is A b2+3aca2α, β are roots of the equation ax2−bx−c=0⇒α+β=ba and αβ=−caα2−αβ+β2=(α+β)2−3αβ =(ba)2−3(−ca) =b2+3aca2Hence, option A.

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