Question

What are the roots of the polynomial equation?

x2−14x−32=0

Answer 1

We are given the quadratic equation :

`x^(2) -14x-32=0`

Now let us use AC method to factorise it.

Step 1:

Find product of A and C

A=1 and C =-32

A*C =-32

Step 2:

Find factors of -32 such that they add up to give -14.

Factors of -32 that add up to give -14 are -16 and 2.

Step 3:

Rewrite the equation using factors found in step 2.

`x^(2) -16x +2x -32 =0`

Step 4:

Factoring by grouping.

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

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

Step 5:

Find roots.

x-16=0 gives x=16

x+2=0 gives x=-2

Answer : Roots of the given Polynomial equation are 16 and -2.

Answer 2

x2−14x−32=0
We can easily factor that into:
(x +2) * (x -16) = 0
x1 = -2
x2 = 16

Answer 3

We are given the quadratic equation :

`x^(2) -14x-32=0`

Now let us use AC method to factorise it.

Step 1:

Find product of A and C

A=1 and C =-32

A*C =-32

Step 2:

Find factors of -32 such that they add up to give -14.

Factors of -32 that add up to give -14 are -16 and 2.

Step 3:

Rewrite the equation using factors found in step 2.

`x^(2) -16x +2x -32 =0`

Step 4:

Factoring by grouping.

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

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

Step 5:

Find roots.

x-16=0 gives x=16

x+2=0 gives x=-2

Answer : Roots of the given Polynomial equation are 16 and -2.