Question

if one zero of the polynomial 2xsquare – 5x – (2k+1 ) is twice the other, then find both the zeroes and the value of k

Answer 1

$hy friend$

Let, p(x)=2x²-5x-(2k+1)--------(1)

Also let, α be one root of (1).

Then the other root will be 2α.

α+2α=-(-5)/2

⇒ 3α=5/2

⇒ α=5/6

Again, α×2α=-(2k+1)/2

⇒ 2α²=-(2k+1)/2

⇒ -(2k+1)/2=2×(5/6)²

⇒ -(2k+1)=4×25/36

⇒ -2k-1=25/9

⇒ -2k=25/9+1

⇒ -2k=34/9

⇒  k=-34/9×1/2

⇒ k=-17/9 Ans.

$thankyou brainly star$