Question

Find the polynomial.

{-1/3, 4} is the solution set of?

A. 3x^2 - 11x + 4 = 0

B. 3x^2 - 11x - 4 = 0

C. 1/3x^2 - 11x - 4 = 0

D.-1/x^2 - 11x - 4 = 0

Answer 1

option B

Explanation:

A.
`3x^2 - 11x + 4 = 0`

3*4 = 12

We find out two factors whose sum is -11 and product is 12

1 times 12 = 12

To get sum -11 , then one factor should be negative. So, factoring is not possible.

B .
`3x^2 - 11x - 4 = 0`

3*(-4) = -12

We find out two factors whose sum is -11 and product is -12

1 times (-12) = -12

1 + (-12) = -11

So two factors are 1 and -12

Split the middle term -11x using factors 1 and -12

So equation becomes

`3x^2 + 1x - 12x - 4 = 0`

Now group first two terms and last two terms

`(3x^2 + 1x)+ (- 12x - 4) = 0`

`x(3x+ 1)-4(3x +1)=0`

(3x+1)(x-4)=0

Now we set each parenthesis =0 and solve for x

3x+1 =0 , subtract 1 on both sides

3x = -1 ( divide both sides by 3)

x= -1/3

Now we set x-4=0

add 4 on both sides

so x=4

Option B is correct

Answer 2

3x^2 - 11x - 4 = 0
(3x + 1)(x - 4) = 0
3x + 1 = 0; x = -1/3
x - 4 = 0; x = 4

{-1/3, 4} is the solution set of 3x^2 - 11x - 4 = 0

answer
B. 3x^2 - 11x - 4 = 0