If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $p(x) = x^2 - ax - b$, then the value of $\alpha^2 + \beta^2$ is:
(a) $a^2 - 2b$
(b) $a^2 + 2b$
(c) $b^2 - 2a$
(d) $b^2 + 2a$

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Accepted Answer

Step 1: $\alpha + \beta = a$, $\alpha\beta = -b$. So $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = a^2 - 2(-b) = a^2 + 2b$

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