Question

if α,β re zeros of quadratic polynomial 2x²+5x+k ,find the value of k such that (α+β)²-αβ=24

Answer 1

hi friend,


if α,β re zeros of quadratic polynomial 2x²+5x+k.

α+ß=-5/2

αß=k/2


given,(α+β)²-αβ=24

(-5/2)²-k/2=24

25/4-k/2=24

25-2k=96

2k=25-96

2k=-71

k=-71/2


I hope this will help u ;)

♥dhathri123♥

Answer 2

HI there !

α,β re zeros of quadratic polynomial 2x²+5x+k.


a = 2
b = 5
c = k

Hence ,
Sum of zeroes = α+ß= - b/a = -5/2

Product of zeroes αß = c/a = k/2

(α+β)²-αβ = 24

(-5/2)²-k/2 =24

25/4 - k/2 =24

25 - 2k= 24 *4
25 - 2k = 96

-2k = 96 - 25

-2k = 71

k = -71/2