Answer:
The zeroes of the given function are -5 and 4.
Step-by-step explanation:
The given function is
[tex]f(x)=x^2+x-20[/tex]
Equate the given function equal to 0, to find the zeroes of the given function.
[tex]x^2+x-20=0[/tex]
Write the middle term as 5x-4x.
[tex]x^2+5x-4x-20=0[/tex]
[tex](x^2+5x)+(-4x-20)=0[/tex]
Taking out common factors from each parenthesis.
[tex]x(x+5)-4(x+5)=0[/tex]
[tex](x-4)(x+5)=0[/tex]
Using zero product property, we get
[tex]x-4=0\Rightarrow x=4[/tex]
[tex]x+5=0\Rightarrow x=-5[/tex]
Therefore the zeroes of the given function are -5 and 4.
