Question

If 4 is a root of x^2-x-w=0 what is the value of w?

Answer 1

Answer:

It is given that -4 is a root of the equation x

2

+px−4=0.

Then, -4 must satisfy the equation,

(−4)

2

+p×(−4)−4=0

16−4p−4=0

4p=12

p=3

Now, the equation x

2

+px+k=0 has equal roots

Therefore,

Discriminant, D=0⟹b

2

−4ac=0

p

2

−4k=0

9−4k=0

k=

4

9

Therefore, p=3 and k=

4

9

.