If - - are the roots of 2 x 2-3 x -4-0- then the equation whose roots are -2 and -2 is- 4 x2-7 x-16-0B- 4 x2-7 x-16-0- 4 x2-7 x-16-0D- 4 x 2-7 x -16-0

The correct option is A 4x^2+7x+16=0Let f(x)=2x^2 3x+4=0 → roots are α, β The equation whose roots are α^2, β^2 is f(√(x))=0 ⇒ 2x 3√(x)+4=0 ⇒ 2x+4=3√(x) ⇒ (2x+ ...

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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 $α^{2}$ and $β^{2}$ is

4 x^{2} + 7 x + 16 = 0

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4 x^{2} - 7 x + 16 = 0

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4 x^{2} + 7 x - 16 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 x^{2} - 7 x - 16 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is A $4 x^{2} + 7 x + 16 = 0$
Let $f (x) = 2 x^{2} - 3 x + 4 = 0 \to$ roots are $α, β$
The equation whose roots are $α^{2}, β^{2}$ is $f (\sqrt{x}) = 0$
$\Rightarrow 2 x - 3 \sqrt{x} + 4 = 0 \Rightarrow 2 x + 4 = 3 \sqrt{x}$
$\Rightarrow (2 x + 4)^{2} = 9 x \Rightarrow 4 x^{2} + 7 x + 16 = 0$

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If α,β are the roots of 2x2−3x+4=0, then the equation whose roots are α2 and β2 is

The correct option is A 4x2+7x+16=0Let f(x)=2x2−3x+4=0→ roots are α,β The equation whose roots are α2,β2 is f(√x)=0 ⇒2x−3√x+4=0⇒2x+4=3√x ⇒(2x+4)2=9x⇒4x2+7x+16=0

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