Question

Which is a zero of the quadratic function f(x) = 16x2 32x − 9?

Answer 1

The given Quadratic function whose zero we have to find is:

`16 x^2 - 32 x -9=0\\\\16x^2-36 x + 4 x -9=0\\\\4 x* (4 x -9)+1 *(4 x -9)=0\\\\(4 x +1)(4 x-9)=0\\\\4 x +1=0 \text{or} ,4 x -9=0\\\\ x=(-1)/(4) \text{or} , x=(9)/(4)`

So,

`x=(-1)/(4) \text{or} , x=(9)/(4)`, are zero of Quadratic function.

If the equation was like this

`\rightarrow 16 x^2 + 32 x -9=0\\\\16 x^2+36 x -4 x -9=0\\\\4 x* (4 x +9)-1 *(4 x +9)=0\\\\(4 x -1)(4 x+9)=0\\\\4 x -1=0 \text{or} ,4 x +9=0\\\\ x=(1)/(4) \text{or} , x=(-9)/(4)`

So,

`x=(1)/(4) \text{or} , x=(-9)/(4)`, are zero of Quadratic function.

Answer 2

A zero of a function is the value of x for which f(x) = 0
f(x) = 16x^2 + 32x - 9 = 0
16x^2 - 4x + 36x - 9 = 0
(16x^2 - 4x) + (36x - 9) = 0
4x(4x - 1) + 9(4x - 1) = 0
(4x + 9)(4x - 1) = 0
4x + 9 = 0 and 4x - 1 = 0
4x = -9 and 4x = 1
x = -9/4 and x = 1/4