Answer: [tex]4x^2 -24x+20[/tex]
Step-by-step explanation:
If p and q are zeroes of f(x), then f(x) = k (x-p)(x-q) , where k is a constant.
Given: The function f(x)f(x) is a quadratic function and the zeros of f(x)f(x) are 1 and 5.
f(x) = k (x-1)(x-5)
y-intercept = Value of function at x=0
So, y-intercept = k (0-1)(0-5)= 5k
Since, y-intercept of f(x) = 20
so, 5k = 20
⇒ k= 4
Quadratic polynomial [tex]= 4(x-1)(x-5)[/tex]
[tex]=4(x^2-6x+5)\\\\= 4x^2 -24x+20[/tex]
Hence, the equation of the quadratic polynomial in standard form =[tex]4x^2 -24x+20[/tex]
