Question

Ishita has asked :- x^3-3x^2-10x+24

Answer 1

hi friend

I hope it helps you

Answer 2

Solution:
There are two methods to solve the third degree polynomials;
1) By grouping &
2) Finding the roots by using the factors of the constant.

BY GROUPING;
x^3-3x^2-10x+24
(x^3 - 3x^2) & (-10x + 24)
or x^2 (x-3) & 2 (-5x+12)
Here, we cannot find the common roots.

BY FACTORS;
Factors of constant 24:
1,2,3,4,6,8,12,24

We shall take each case & try to find the common roots.

Take x = 1
Therefore, (1^3) - 3 × (1^2) - 10 × (1) + 24
= 1-3-10+24
= 12
LHS doesn't equals RHS.
Hence discarded.

Take x = 2
Therefore, (2^3) - 3 × (2^2) - 10 × (2) + 24
= 8-12-20+24
= 0
LHS equals RHS.
Hence, (x-2) is our root.
Let us see if we can factor out the rest of the equation.

Make, x^3-3x^2-10x+24
= x^3 -2x^2 -x^2 +2x -12x +24
Therefore, we can take the commons,
x^2 (x-2) - x (x-2) - 12 (x-2) = 0
or (x-2) (x^2 -x -12) = 0
or (x-2) (x-4) (x+3) = 0

Therefore, x = 2
or x = 4
or x = -3
is required solution.

Hope you got it!