Question

If alpha and beta are zeroes of the polynomial 2x²-3x+k such that alpha-beta =1, find the value of k.

Answer 1

Answer:

k = 5/8

Step-by-step explanation:

α and β are zeroes of the polynomial 2x²-3x+k

a= coefficient of x² = 2

b = coefficient of x = -3

c = constant term = k

Sum of zeros = α+β = -b/a = - (-3/2) = 3/2

Product of zeros = αβ = c/a = k/2

(α-β)² = (α+β)²-4αβ

putting the values of (α-β) = 1, (α+β) = 3/2 and αβ = k/2

1² = (3/2)² - 4 × (k/2)

1 = (9/4) -(4k/2)

1 = (9/4) - 2k

1-(9/4) = -2k

(4-9)/4 = -2k

-5/4 = -2k

2k = 5/4

k = (5/4) × (1/2)

k = 5/8