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Relation between Roots and Coefficients for Quadratic

If α, β are t...

Question

If $α, β$ are the root of a quadratic equation $x^{2} - 3 x + 5 = 0$ , then the equation whose roots are $(α^{2} - 3 α + 7) and (β^{2} - 3 β + 7)$ is

A

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

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B

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

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C

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

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D

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

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Solution

The correct option is B $x^{2} - 4 x + 4 = 0$
Given $α, β$ are the roots of equation $x^{2} - 3 x + 5 = 0$
So,
$α^{2} - 3 α + 5 = 0 β^{2} - 3 β + 5 = 0$
$∴ α^{2} - 3 α = - 5 and β^{2} - 3 β = - 5$
Now,
$α^{2} - 3 α + 7 = 2 and β^{2} - 3 β + 7 = 2$

Hence, the quadratic equation whose roots are $2, 2$ is
$(x - 2)^{2} = 0 ∴ x^{2} - 4 x + 4 = 0$

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Relation between Roots and Coefficients for Quadratic

Standard XIII Mathematics

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