Answer :
The zeros of given function [tex]y=x^{2}+8 x+15[/tex] is – 5 and – 3
Solution:
[tex]\text { Given, equation is } y=x^{2}+8 x+15[/tex]
We have to find the zeros of the function by rewriting the function in intercept form.
By using intercept form, we can put value of y as to obtain zeros of function
We know that, intercept form of above equation is [tex]x^{2}+8 x+15=0[/tex]
[tex]\text { Splitting } 8 x \text { as }(5+3) x \text { and } 15 \text { as } 5 \times 3[/tex]
[tex]\begin{array}{l}{\rightarrow x^{2}+(5+3) x+5 \times 3=0} \\\\ {\rightarrow x^{2}+5 x+3 x+5 \times 3=0}\end{array}[/tex]
Taking “x” as common from first two terms and “3” as common from last two terms
x (x + 5) + 3(x + 5) = 0
(x + 5)(x + 3) = 0
Equating to 0 we get,
x + 5 = 0 or x + 3 = 0
x = - 5 or – 3
Hence, the zeroes of the given function are – 5 and – 3