Zeros of quadratic polynomial [tex]f(x)=-x^{2}+13 x-36[/tex] are 4 and 9
Solution:
Need to determine zero of the function [tex]f(x)=-x^{2}+13 x-36[/tex]
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).
[tex]\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}[/tex]
Hence zeros of quadratic polynomial [tex]f(x)=-x^{2}+13 x-36[/tex] are 4 and 9
