Question

Two is a zero of the equation x^3−x^2−14x+24=0.

Answer 1

Answer:

The factored form is equivalent to the given equation is (x - 2) (x - 3) (x + 4).

Step-by-step explanation:

Since 2 is a zero of the equation $x^{3} - x^{2} -14x + 24 = 0$

Therefore, (x - 2) is a factor of the equation $x^{3} - x^{2} -14x + 24 = 0$

Now, on dividing $x^{3} - x^{2} -14x + 24 = 0$ by (x - 2) we get,

$(x - 2) (x^{2} + x - 12)$ as shown in Fig(1)

On factorising x² + x - 12

= x² + x - 12

=  x² + 4x - 3x - 12

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

= (x - 3) (x + 4)

Now, $(x - 2) (x^{2} + x - 12)$ = $(x - 2) (x -3) (x + 4)$

So the factored form is equivalent to the given equation is (x - 2) (x - 3) (x + 4). Therefore option (c) is the correct answer.