If - are the roots of the equation ax2 -2bx -c - 0 and - - are the roots of Ax2 - 2Bx - C- 0 - then b2 -ac-B2 -AC -

Α,β are the roots of the equation ax^2 +2bx +c = 0 = gt; |α β |= √(b^2 ac)/|a| α+δ, β+δ are the roots of Ax^2+ 2Bx + C= 0 = gt; |α+δ β+δ| =√(b^2 4ac)/ ...

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Byju's Answer

Standard XI

Mathematics

Relations Between Roots and Coefficients

If α,β are th...

Question

If $α, β$ are the roots of the equation a $x^{2}$ +2bx +c = 0 and $α + δ$ , $β + δ$ are the roots of A $x^{2}$ + 2Bx + C= 0 , then $\frac{b^{2} - a c}{B^{2} - A C}$ =

$\frac{a}{A}$

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

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$\frac{A}{a}$

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

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Solution

The correct option is D
$(\frac{a}{A})^{2}$

$α, β$ are the roots of the equation $a x^{2} + 2 b x + c$ = 0 => | $α - β$ |= $\frac{\sqrt{b^{2} - a c}}{| a |}$

$α + δ$ , $β + δ$ are the roots of $A x^{2} + 2 B x + C$ = 0 => | $α + δ$ - $β + δ$ | = $\frac{\sqrt{b^{2} - 4 a c}}{| a |}$

$\frac{b^{2} - a c}{a^{2}}$ = $\frac{B^{2} - A C}{A^{2}}$ => $\frac{b^{2} - a c}{B^{2} A C}$ = $\frac{a^{2}}{A^{2}}$

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If α, β are the roots of a $x^{2}$ +2bx+c=0 and a+δ, β+δ are the roots of A $x^{2}$ + 2Bx + C=0 then $\frac{b^{2} - a c}{B^{2} - A c}$ is

If $α, β$ are the roots of the equation a $x^{2}$ +2bx +c = 0 and $α + δ$ , $β + δ$ are the roots of A $x^{2}$ + 2Bx + C= 0 , then $\frac{b^{2} - a c}{B^{2} - A C}$ =