Question

What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?

Answer 1

we have

`f(x)=2x^(2)+16x-9`

To find the zeros equate the function to zero

`2x^(2)+16x-9=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`2x^(2)+16x=9`

Factor the leading coefficient

`2(x^(2)+8x)=9`

Complete the square. Remember to balance the equation by adding the same constants to each side

`2(x^(2)+8x+16)=9+32`

`2(x^(2)+8x+16)=41`

Rewrite as perfect squares

`2(x+4)^(2)=41`

`(x+4)^(2)=(41/2)`

Square root both sides

`x+4=(+/-)\sqrt{(41)/(2)}`

`x=-4(+/-)\sqrt{(41)/(2)}`

therefore

the answer is

The zeros of the function are

`x=-4+\sqrt{(41)/(2)}`

`x=-4-\sqrt{(41)/(2)}`