Question

Check the values of x from the given options for which the polynomial $x^3-7x^2+14x-8$ vanishes.

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A), (B), (D)

The correct options are
A 1
B 2
D 4

For the polynomial to vanish, we should equate it to zero.
So, the equation we get is,
$x^3-7x^2+14x-8=0$
For checking which of the given option satisfies the equation, substitute each of the options one by one in the equation.

On substituting x = 1;

$=1^3-7(1{)}^2+14(1)-8=1-7+14-8=0$
On substituting x = 2;

$=(2{)}^3-7(2{)}^2+14\left(2\right)-8=8-28+28-8=0$

On substituting x = 3;

$=(3{)}^3-7(3{)}^2+14\left(3\right)-8=27-63+42-8=69-71=-2$

On substituting x = 4;

$=(4{)}^3-7(4{)}^2+14\left(4\right)-8=64-112+56-8=120–120=0$

So, the values 1, 2, 4 satisfy the given equation and thus make the polynomial $x^3-7x^2+14-8$ vanish.