Question

If alpha and beta are the zeros of the polynomial 6x2-5x+k such that alpha-beta=1/6 then find the value of k

Answer 1

Answer:

k = 1

Step-by-step explanation:

sum of roots = $\frac{5}{6}$

product of roots = $\frac{k}{6}$

∴ α + β = $\frac{5}{6}$

αβ = $\frac{k}{6}$

(α-β)² = (α+β)² - 4αβ

( $\frac{1}{6}$ )² = ( $\frac{5}{6}$ )² - 4 ( $\frac{k}{6}$ )

$\frac{k}{6}$ = $\frac{1}{6}$

k = 1