If - - be the roots of a x2-2 b x-c-0 and - - be those of A x2-2 B x-C-0- then the value of b2-a c-B2-A C

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Relations between Roots and Coefficients : Higher Order Equations

If α, β be th...

Question

If $α, β$ be the roots of $a x^{2} + 2 b x + c = 0$ and $α + δ, β + δ$ be those of $A x^{2} + 2 B x + C = 0$ , then the value of $\frac{(b^{2} - a c)}{(B^{2} - A C)}$ is

{(\frac{a}{A})}^{2}

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{(\frac{a}{a})}^{2}

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Solution

The correct option is A ${(\frac{a}{A})}^{2}$
If the roots of 2nd eqn. be $α^{1}, β^{1}$ then
$α^{1} - β^{1} = (α + δ) - (β + δ)$
$(α^{1} + β^{1})^{2} - 4 α^{1} β^{1} = (α + β)^{2} - 4 α β$
$\frac{4 b^{2} - 4 a c}{a^{2}} = \frac{4 B^{2} - 4 A C}{A^{2}} \Rightarrow \frac{b^{2} - a c}{B^{2} - A C} = \frac{a^{2}}{A^{2}}$

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Similar questions

Q. If

α, β

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and

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for some constant

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

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If α,β be the roots of ax2+2bx+c=0 and α+δ,β+δ be those of Ax2+2Bx+C=0, then the value of (b2−ac)(B2−AC) is

The correct option is A (aA)2If the roots of 2nd eqn. be α1,β1 then α1−β1=(α+δ)−(β+δ) (α1+β1)2−4α1β1=(α+β)2−4αβ 4b2−4aca2=4B2−4ACA2⇒b2−acB2−AC=a2A2

If $α, β$ be the roots of $a x^{2} + 2 b x + c = 0$ and $α + δ, β + δ$ be those of $A x^{2} + 2 B x + C = 0$ , then the value of $\frac{(b^{2} - a c)}{(B^{2} - A C)}$ is