Question

What is/are the x-intercepts of the graph y = 2x³ + x² - 7x - 6?A. (-3/2,0), (-1,0), (2,0)B. (-1,0), (-2/3,0), (2,0)OC. (-2,0), (2/3,0), (1,0)OD. (-2,0), (1,0), (3/2,0)Reset Selection

Answer 1

Given that

We have an equation as

`y=2x^3+x^2-7x-6`

Explanation -

Here we have to find the values of x when y = 0.

So we will use HINT AND TRIAL METHOD.

In this, we will substitute such values of x that make y = 0.

So first we will put x = -1

`\begin{gathered} y=2(-1)^3+(1)^2-7(-1)-6 \\ y=-2+1+7-6=8-8=0 \end{gathered}`

So the first point will be (-1,0)

Now we will substitute x = 2

`\begin{gathered} y=2(2)^3+2^2-7*2-6 \\ y=16+4-14-6=20-20 \\ y=0 \end{gathered}`

So the second point is (2,0)

Now we will substitute x = -3/2

`\begin{gathered} y=2*(-(3)/(2))^3+(-(3)/(2))^2-7(-(3)/(2))-6 \\ y=(2*-27)/(8)+(9)/(4)+(21)/(2)-6 \\ y=-(54)/(8)+(9)/(4)+(21)/(2)-6=-(27)/(4)+(9)/(4)+(21)/(2)-6 \\ y=-(18)/(4)+(21)/(2)-6=-(9)/(2)+(21)/(2)-6 \\ y=(12)/(2)-6=6-6=0 \end{gathered}`

So the third point is (-3/2,0)

Hence option A is correct.

And the final answer is (-1,0), (2,0), (-3/2,0)