If - - are the roots of the equation ax 2-2 bx - c -0 and - - are the roots of Ax 2-2 Bx - C -0- then b 2- ac - B 2- AC -A- a - AB- A - aC- a - A 2D- A - a 2

The correct option is C (a / A)2 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 ...

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Byju's Answer

Standard XII

Mathematics

Quadratic Formula for Finding Roots

If α, β are t...

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

a / A

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A / a

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(a / A)²

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(A / a)²

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Solution

The correct option is C
(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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Similar questions

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

Q. 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

for some constant

δ

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

Q. If

α, β

are the roots of

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

and

α + δ

β δ

are the roots of

A x^{2} + 2 B x + C = 0

, then

Q. If

α, β

are the roots of

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

and

α + β, α^{2} + β^{2}, α^{3} + β^{3}

are in G.P., where

△ = b^{2} - 4 a c

, then

Q. If

α, β, γ, δ

are in GP where

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are roots of the equation

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If α,β are the roots of the equation ax2 +2bx +c = 0 and α+δ, β+δ are the roots of Ax2 + 2Bx + C= 0 , then b2–acB2–AC =

The correct option is C (a / A)2 α,β are the roots of the equation ax2+2bx+c = 0 => |α−β |= √b2−ac|a| α+δ, β+δ are the roots of Ax2+2Bx+C= 0 => |α+δ - β+δ| =√b2−4ac|a| b2–aca2 = B2–ACA2 => b2–acB2AC= a2A2

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