If - - are the roots of 2 x 2-3 x -4-0- then the equation whose roots are 2 - 2 - isA- x2-3 x-4-0B- x2-3 x-8-0C- 4 x2-3 x-4-0D- 4 x2-3 x-2-0

The correct option is B x^2+3x+8=0f(x) = 2x^2+3x+4 f(x)=0 →α, β are the roots The equation whose roots are 2α, 2β is, f (x2)= 0 ⇒ 2 (x2)^2+ 3 nbsp;(x2)+4 = ...

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Standard XII

Mathematics

Relation between Roots and Coefficients for Quadratic

If α, β are t...

Question

If $α, β$ are the roots of $2 x^{2} + 3 x + 4 = 0$ , then the equation whose roots are $2 α, 2 β$ is

x^{2} + 3 x + 4 = 0

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x^{2} + 3 x + 8 = 0

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4 x^{2} + 3 x + 4 = 0

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4 x^{2} + 3 x + 2 = 0

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Solution

The correct option is B $x^{2} + 3 x + 8 = 0$
$f (x) = 2 x^{2} + 3 x + 4 f (x) = 0 \to α, β are the roots$
The equation whose roots are $2 α, 2 β$ is,
$f (\frac{x}{2}) = 0$
$\Rightarrow 2 {(\frac{x}{2})}^{2} + 3 (\frac{x}{2}) + 4 = 0 \Rightarrow x^{2} + 3 x + 8 = 0$

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The correct option is B x2+3x+8=0f(x)=2x2+3x+4f(x)=0→α,β are the roots The equation whose roots are 2α,2β is, f(x2)=0 ⇒2(x2)2+3(x2)+4=0⇒x2+3x+8=0

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The correct option is B $x^{2} + 3 x + 8 = 0$
$f (x) = 2 x^{2} + 3 x + 4 f (x) = 0 \to α, β are the roots$
The equation whose roots are $2 α, 2 β$ is,
$f (\frac{x}{2}) = 0$
$\Rightarrow 2 {(\frac{x}{2})}^{2} + 3 (\frac{x}{2}) + 4 = 0 \Rightarrow x^{2} + 3 x + 8 = 0$