If the sum of the squares of zeroes of the quadratic polynomial $f(x) = x^2 - 8x + k$ is 40, find the value of $k$.

Question

Accepted Answer

Step 1: Let the zeroes of polynomial $f(x)$ be $\alpha$ and $\beta$. $\alpha + \beta = 8$ and $\alpha\beta = k$
Step 2: $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = 40 \Rightarrow 64 - 2k = 40 \Rightarrow k = 12$

Question

Solution