Question

If alpha and Beta are the zeros of polynomial p(x) = x²– 5x +4, find the value of 1/alpha +1/beta-2alpha.beta​

Answer 1

Answer:

· If alpha and beta are the zeros of polynomial p (x) =x^2 - 5x +4 , then what is the value of 1÷alpha + 1÷beta -2alpha

Answer 2

given polynomial :- x² - 5x + 4

to find the value of 1/alpha +1/beta-2alpha.beta, first we needa find the zeroes (alpha and beta) of the given polynomial.

let us find them by splitting the middle term method.

= x² - 5x + 4

= x² - (4x + x) + 4

= x² - 4x - x + 4

= x(x - 4) - 1(x - 4)

= (x - 4) (x - 1)

equating both factors by 0

• x - 4 = 0

➡ x = 4

• x - 1 = 0

➡ x = 1

hence, alpha = 4 and beta = 1

now value of 1/alpha +1/beta-2alpha.beta

= 1/4 + 1/1 - 2(4 × 1)

= 1/4 + 4/4 - 2(4)

= 5/4 - 8

LCM of 4 and 1 = 4 × 1 = 4

= 5/4 - (8 × 4)/(1 × 4)

= 5/4 - 32/4

= -27/4 final answer.