Question

Select the correct answer from the drop-down menu. Find the polynomial.-1/3, 4 is the solution set of.

1. 3x^2-11x+4=0
2. 3x^2-11x-4=0
3.1/3x^2-11x-4=0
4.-1/3x^2-11x-4=0

Answer 1

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

Explanation:

Since
`x=-(1)/(3)` and
`x=4` is a solution; then we can work backwards to find the required polynomial.

Thus;

`3x+1=0` and
`x-4=0`

We multiply the left hand side and right hand side separately to obtain;

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

We expand using the distributive property to obtain;

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

Simplify;

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

The second choice is correct.

Answer 2

3x² - 11x - 4 =0

Explanation:

The solution to the polynomial is;

X= -1/3 and x = 4

For x = -1/3, we have (x + 1/3) = 0

For x = 4, we have (x - 4) = 0

Combining the two equations we have;

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

Now expand the equation

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

x² - 4x + 1/3x - 4/3 = 0

Multiplying by 3 to eliminate the denominator,

3x² - 12x + x - 4 = 0

3x² - 11x - 4 =0