which function has zeros at x = -2 and x = 5?\n○ f(x)=x² + 2x - 10\n○ f(x)=x² - 2x - 10\n○ f(x)=x² + 3x…

which function has zeros at x = -2 and x = 5?\n○ f(x)=x² + 2x - 10\n○ f(x)=x² - 2x - 10\n○ f(x)=x² + 3x - 10\n○ f(x)=x² - 3x - 10

which function has zeros at x = -2 and x = 5?\n○ f(x)=x² + 2x - 10\n○ f(x)=x² - 2x - 10\n○ f(x)=x² + 3x - 10\n○ f(x)=x² - 3x - 10

Answer

Explanation:

Step1: Recall zero - product property

If (x = a) and (x = b) are zeros of a quadratic function, then the function can be written in factored form as (f(x)=(x - a)(x - b)). Here (a=-2) and (b = 5), so (f(x)=(x+2)(x - 5)).

Step2: Expand the factored form

Using the FOIL method ((x + 2)(x - 5)=x\times x+x\times(-5)+2\times x+2\times(-5)=x^{2}-5x + 2x-10).

Step3: Simplify the expression

Combining like - terms, (x^{2}-5x + 2x-10=x^{2}-3x - 10).

Answer:

(f(x)=x^{2}-3x - 10) (the fourth option)