Question

If alfa and bitta are the zeroes of polynomial f(x) =x^2-4x-5 then find the value of alfa^2 + bitta^2? ​

Answer 1

Answer:

α and β are zeroes of the polynomial f(x) = x2 – 4x – 5

$\alpha + \beta = \frac{ - ( - 4)}{1} = 4$

$\alpha \times \beta = \frac{ - 5}{1} = - 5$

${( \alpha + \beta )}^{2} = { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta$

${4}^{2} = { \alpha }^{2} + { \beta }^{2} + 2( - 5)$

$16 - 10 = { \alpha }^{2} + { \beta }^{2}$

${ \alpha }^{2} + { \beta }^{2} = 26$