which function has real zeros at ( x = - 8 ) and ( x = 5 )?\n( g(x)=x^{2}+3x - 40 )\n( g(x)=x^{2}+3x + 40…

which function has real zeros at ( x = - 8 ) and ( x = 5 )?\n( g(x)=x^{2}+3x - 40 )\n( g(x)=x^{2}+3x + 40 )\n( g(x)=x^{2}+14x - 40 )\n( g(x)=x^{2}+14x + 40 )

which function has real zeros at ( x = - 8 ) and ( x = 5 )?\n( g(x)=x^{2}+3x - 40 )\n( g(x)=x^{2}+3x + 40 )\n( g(x)=x^{2}+14x - 40 )\n( g(x)=x^{2}+14x + 40 )

Answer

Explanation:

Step1: Use the zero - product property

If (x = a) and (x = b) are zeros of a quadratic function (y=(x - a)(x - b)). Here (a=-8) and (b = 5), so (y=(x+8)(x - 5)).

Step2: Expand the product

Use the FOIL method: ((x+8)(x - 5)=x\times x+x\times(-5)+8\times x+8\times(-5)). [ \begin{align*} (x + 8)(x-5)&=x^{2}-5x+8x-40\ &=x^{2}+( - 5 + 8)x-40\ &=x^{2}+3x-40 \end{align*} ]

Answer:

(g(x)=x^{2}+3x - 40) (the first option)