Question

Which function has zeros at x = -2 and x = 5?

O f(x) = x2 + 2x - 10
• f(x) = x2 - 2x - 10
O f(x) = X2 + 3x - 10
® f(x) = x2 - 3x - 10

Answer 1

f(x)=x²-3x-10

Explanation:

\begin{gathered}f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5\end{gathered}

f(x)=x

2

−3x−10

tofindxinterceptorzerosubstitutef(x)=0

0=x

2

−3x−10

x

2

−3x−10=0

x

2

+2x−5x−10=0

x(x+2)−5x−10=0

x(x+2)−5(x+2)=0

(x+2).(x−5)=0

x+2=0

x−5=0

x=−2

x=5

therefore the zeros of the equation are x₁=-2,x₂=5