If alpha and beta are the zeros of the Q P f(x) = x2-4x+3 Find the value of alpha4beta3+alpha3beta4 - Maths - Polynomials

Question

If alpha and beta are the zeros of the Q P f(x) =
x2-4x+3 Find the value of
alpha4beta3+alpha3beta4

Ajanta Trivedi · Accepted Answer

the given polynomial is $f (x) = x^{2} - 4 x + 3$

if $α a n d β$ are the zeroes of f(x).

$α + β = - (- 4) α + β = 4............. (1) α β = 3............ (2)$

therefore

$α^{4} β^{3} + α^{3} β^{4} = α^{3} β^{3} (α + β) = (α β)^{3} (α + β) = 3^{3} * 4 = 27 * 4 = 108$

hope this helps you.

cheers!!

If alpha and beta are the zeros of the Q.P f(x) = x2-4x+3. Find the value of alpha4beta3+alpha3beta4