Question

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

Solution

## p (x)= x^2-4x+kp (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 ----1sum of zeroes=> a+b = -B/A = -(-4)/1 = 4Product of zeroes => a*b = C/A  = kSubstitute these values in the equation 1 we get=> 4^2 - 2k = 20=> 16 - 2k = 20=> 2k = -4=> k = -2therefore the value of k is -2Mathematics

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