Question

Find The Zero Of The Function
F (x)=x^2+3x-10
And
F (x)=-x^2+8x+9

Answer 1

1)
$F(x)=x^2+3x-10 \\ 0=x^2+3x-10 \\ 0=x^2-2x+5x-10 \\ 0=x(x-2)+5(x-2) \\ 0=(x+5)(x-2) \\ x+5=0 \ \lor \ x-2=0 \\ x=-5 \ \lor \ x=2 \\ \\ \hbox{the function has two zeroes: x=-5 and x=2}$

2)
$F(x)=-x^2+8x+9 \\ 0=-x^2+8x+9 \\ 0=-x^2-x+9x+9 \\ 0=-x(x+1)+9(x+1) \\ 0=(-x+9)(x+1) \\ -x+9=0 \ \lor \ x+1=0 \\ x=9 \ \lor \ x=-1 \\ \\ \hbox{the function has two zeroes: x=-1 and x=9}$

Answer 2

f(x)=x²+3x-10,

When f(x)=0,

x²+3x-10=0

(x+5)(x-2)=0

x=-5 and x=2.

------------------------

g(x)=-x²+8x+9

When g(x)=0,

(x+1)(9-x)=0

x=-1, x=9.