Question

Consider the quadratic function f(x)=-2x^2+12x+32=0.

Answer 1

Answer:

the solution of given quadratic function is x = -2 and x=8

Step-by-step explanation:

Step:-1

Given quadratic function is $-2 x^{2} +12 x+32=0$

Taking common '-2' term is

$-2 (x^{2} -6 x+-16)=0$

dividing '-2' on both sides we get,

$( x^{2} -6 x -16)=0$

Now finding factors 16 = 8 X 2

$x^{2} - 8 x + 2 x - 16 =0$

$x( x-8)+2(x-8) = 0$

$(x-8)(x+2)=0$

$x - 8 = 0 and x+2 =0$

x = 8 and x=-2

Answer 2

Answer: the solutions are

x = 8

x = - 2

Step-by-step explanation:

The given quadratic function is expressed as

f(x) = -2x² + 12x + 32 = 0

Since 2 is a common factor of the function, we would divide through by 2, it becomes

- x² + 6x + 16 = 0

Next, we would find two numbers such that their sum or difference is 6x and their product is - 16x^2. The two numbers are 8x and -2x. Therefore,

- x² + 8x - 2x + 16 = 0

- x(x - 8) - 2(x - 8) = 0

(x - 8)(- x - 2) = 0

x - 8 = 0 or - x - 2 = 0

x = 8 or x = - 2