Question

if the squared difference of the zeros of quadratic polynomial P(x) = x²+ 3x + k is 3, find k​

Answer 1

If A and B are the zeros of the polynomial f(x)=x2-5x+k such that alpha minus beta =1, what is the value of k?

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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 = (1)2

=> (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.