Question

If alpha and beta are the zeroes of the polynomial x^2-5x+m such that alpha -beta=1, find m

Answer 1

Hey

Here is your answer,

x2-5x+m=0
Here, a=1, b=-5 and c=km

Now, α+ β = -b/a= -(-5)/1= 5
α x β = c/a= m/7= m

Now,α - β =1

Squaring both sides, we get,

(α - β)2=12

⇒ α2 + β2 - 2αβ = 1
⇒ (α2 + β2 + 2αβ) - 4αβ = 1
⇒ (α +β)2 -4αβ =1
⇒ (5)2-4m=1
⇒ -4m= 7-25
⇒ -4m= -24
⇒ m=6

So the value of m is 6.

Hope it helps you!