Question

What are the zero functions of F(x) = -x^2 + 13X -36

Answer 1

Zeros of quadratic polynomial
`f(x)=-x^(2)+13 x-36` are 4 and 9

Solution:

Need to determine zero of the function
`f(x)=-x^(2)+13 x-36`

Zero of the function are those values of x for which f(x) is equal to zero.

So need to solve following expression for x to get zeros of f(x).

`\begin{array}{l}{-x 2+13 x-36=0} \\\\ {\Rightarrow-x 2+9 x+4 x-36=0} \\\\ {\Rightarrow-x(x-9)+4(x-9)=0} \\\\ {\Rightarrow(-x+4)(x-9)=0} \\\\ {\Rightarrow(-x+4)(x-9)=0} \\\\ {\text { When }(-x+4)=0 \text { or }(x-9)=0} \\\\ {\Rightarrow-x=-4} \\\\ {\Rightarrow x=4} \\\\ {\Rightarrow x=4} \\\\ {\text { When }(x-9)=0} \\\\ {\Rightarrow x=9}\end{array}`

Hence zeros of quadratic polynomial
`f(x)=-x^(2)+13 x-36` are 4 and 9