If - and - are the roots of x2 - ax - b2 - 0- then -2 - -2 is equal to

The correct option is A a^2 2b^2 Given equation: x^2 ax+b^2=0 Sum of roots, α+β=a and #160;Product of roots, αβ=b^2 α^2+β^2=(α+β) ...

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Standard X

Mathematics

Roots of Quadratic Equation

If α and ...

Question

If $α$ and $β$ are the roots of $x^{2} - a x + b^{2} = 0$ , then $α^{2} + β^{2}$ is equal to

a^{2} + 2 b^{2}

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a^{2} - 2 b^{2}

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a^{2} - 2 b

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a^{2} + 2 b

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a^{2} - b^{2}

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Solution

The correct option is A $a^{2} - 2 b^{2}$
Given equation: $x^{2} - a x + b^{2} = 0$

Sum of roots, $α + β = a$ and

Product of roots, $α β = b^{2}$

$α^{2} + β^{2} = (α + β)^{2} - 2 α β$

$\Rightarrow α^{2} + β^{2} = a^{2} - 2 b^{2}$

Hence, B is the correct option.

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