Question

if alpha and beta are the zeros of the quadratic polynomial f(x) = x^2-4x+3 . find the value of alpha^4*beta^2+alpha^2*beta^4

Answer 1

$here \\ f(x) = {x}^{2} - 4x + 3 \\ = {x}^{2} - x - 3x + 3 \\ = x(x - 1) - 3(x - 1) \\ = (x - 3)(x - 1) \\either \: x - 3 = 0 \\ = > x = 3 \\ or \: x - 1 = 0 \\ = > x = 1 \\ therefore \: \alpha = 3 \: and \: \beta = 1 \\ now \: { \alpha }^{4} \times { \beta }^{2} + { \alpha }^{2} \times { \beta }^{4} = {3}^{4} \times {1}^{2} + {3}^{2} + {1}^{4} \\ = 81 \times 1 + 9 \times 1 \\ = 90$

Answer 2

Answer:

Step-by-step explanation: