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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+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


Mathematics

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