Question

one root of the the quadratic equation 2x2-8x-k is 5/2. find the other root and the value of k

Answer 1

Hi,

α+β = -b/a
β = -b/a - α
β = -(-8)/2 - 5/2
β = 4 - 5/2
β = 3/2

For the value of k,
2x²-8x-k = 0
2(3/2)²-8(3/2) = k
18/4-12 = k
⇒k = 18-48/4
⇒k = -30/4
⇒k = -15/4

hope it helps u!!

Answer 2

Answer: other root = 3/2, k = -15/2

Step-by-step explanation:

α + β = -b/a

5/2 + β = - (-8)/2

β = 8/2 - 5/2

β = 3/2

Since 5/2 is a root of 2x² - 8x - k, therefore putting x=5/2 in the eq.n will be =0

Substituting value of x..

2(5/2)² - 8(5/2) - k = 0

k = -15/2

Similarly, if we put x= 3/2, then also k will be = -15/2.