Question

If α and β are the zeroes of quadratic polynomial f(x)=x^2-4x+3,find the value of (α^4β^2+α^2β^4)

Answer 1

First let us take out the zeroes of the quadratic polynomial: x^2 - 4x + 3

Solving by middle term splitting => x^2 - 4x + 3 = 0 => x^2 -x -3x + 3 = 0=> x(x-1) -3(x-1) = 0=> (x-3)(x-1) = 0

• Alpha = 3

• Beta = 1

Value of the given expression will be : 3^4*1^2 + 3^2*1^4 Answer : 90

Answer 2

Answer:

90

Step-by-step explanation:

x²-4x+3

x² - 3x - x + 3

x(x-3) - 1 (x-3)

(x-1) (x-3)

x=1 x=3

alpha = 1 , beta = 3

alpha⁴beta²+ alpha²beta⁴

(1)⁴(3)² + (1)²(3)⁴

1×9 + 1×81

9 + 81

=90