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.