Question

If sum of the square of zeros of the quadratic polynomial $f\left(x\right)=x^2-4x+k$ is $20$, then find the value of $k$.

Answer 1

p (x)= x^2-4x+k

p (x)=Ax^2+Bx+C(The equation is in this form)

Let the zeroes be 'a' and 'b'

It is given that

=> a^2+b^2= 20

=> (a+b)^2 - 2ab = 20 ----1

sum of zeroes

=> a+b = -B/A = -(-4)/1 = 4

Product of zeroes

=> a*b = C/A = k

Substitute these values in the equation 1 we get

=> 4^2 - 2k = 20

=> 16 - 2k = 20

=> 2k = -4

=> k = -2

therefore the value of k is -2