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

Correct answer: (A) a^2-2 b^2. Given equation, x^2-a x+b^2=0 arrow(1) We know that, sum of the roots is given by α+β=a and the product of the roots is given by α β=b^2 Now, α^2+β^2=(α+β)^2-2 α β =a^2-2 b^2

Q65 / 180 · KCET 2015 · Mathematics

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

Correct answer
A
$ a^{2}-2 b^{2} $
B
$ 2 a^{2}-b^{2} $
C
$ a^{2}-b^{2} $
D
$ a^{2}+b^{2} $

Solution

Given equation, $x^{2}-a x+b^{2}=0 \rightarrow(1)$ We know that, sum of the roots is given by $\alpha+\beta=a$ and the product of the roots is given by $\alpha \beta=b^{2}$ Now, $\alpha^{2}+\beta^{2}=(\alpha+\beta)^{2}-2 \alpha \beta$ $=a^{2}-2 b^{2}$

Hence, the correct answer is option: 'A'.

If \( \alpha \) and \( \beta \) are the roots of \( x^{2}-a x+b^{2}=0 \), then \( \alpha^{2}+\beta^{2} \) is equal to

Solution

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