Question

if alpha and beta are zeros of polynomial F(X) = x square - 5 + 3 and Alpha minus beta =1,than find k

Answer 1

hey dear user!!!!
your answer ⤵⤵

α+β= 5

αβ=k

α - β =1

(α - β)2 = 1

(α + β)2 - 4αβ = 1

52 - 4k = 1

25-4k=1

4k=24

k=6
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✖✖✖✖or ✖✖✖✖

 x2-5x+k

Here, a=1, b=-5 and c=k

Now, alpha+beta= -b/a= -(-5)/1= 5

alpha*beta= c/a= k/1= k

Now, apha-beta=1

Squaring both sides, we get,

(alpha-beta)2=12

=> (alpha+beta)2-4*aplha*beta=1

=> (5)2-4k=1

=> -4k= 1-25

=> -4k= -24

=> k=6

So the value of k is 6.

Hope it helps!!

Cheers!
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