Question

The graph of a polynomial f(x) = (2x - 3)(x - 4)(x + 3) has x-intercepts at 3 x values. What are
they?

Answer 1

f(x) = (2x-3)(x-4)(x+3)
x-intercept, let f(x) = 0
0 = 2x-3
3 = 2x
x = 3/2
—
0 = x-4
x = 4
—
0 = x+3
x = -3
Therefore the 3 x-intercepts are (3/2,0) , (4,0) and (-3,0)

Answer 2

The x-intercepts of a function are the points where the function crosses the x-axis.

The x-intercepts are $\mathbf{ \frac 32, 4, and -3 }$

The polynomial is given as:

$f(x) = (2x - 3)(x -4)(x + 3)$

Equate the polynomial to 0

$(2x - 3)(x -4)(x + 3) = 0$

Split the polynomial

$2x - 3 = 0$    or    $x -4 = 0$    or    $x + 3 = 0$

Solve for x in all cases

$x = \frac 32$    or $x = 4$ or $x=-3$

Hence, the x-intercepts are $\mathbf{ \frac 32, 4, and -3 }$

Read more about intercepts at:

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