Question

(x – 3) is the factor of polynomial (x³– 3x²+ ax – 10) then find the value of ‘a'.​

Answer 1

Given:

Polynomial

$x^3- 3x^2+ ax - 10$ has a factor ($x-3$).

To find:

Value of a = ?

Solution:

First of all, let us learn about the concept of factors.

Let us consider a quadratic equation for this.

$x^2 -5x+ 6$

Let us factorize it.

$x^2 -5x+ 6\\\Rightarrow x^2 -2x-3x+ 6\\\Rightarrow x(x -2)-3(x -2)\\\Rightarrow (x -2)(x -3)$

Now, the two factors are $(x-2)$ and $(x-3)$.

Let us put the value of x = 2 and x = 3 one by one and let us find the value of the quadratic equation.

$x =2 \Rightarrow 2^2 -5 \times 2 +6 = 10 -10 =0\\x =3 \Rightarrow 3^2 -5 \times 3 +6 = 15 -15 =0$

That means "If (x-k) is a factor of polynomial, then putting the value of x = k will make the polynomial equal to 0."

Now, we are given that:

$x^3- 3x^2+ ax - 10$ has a factor ($x-3$).

Let us put x = 3 the polynomial will become equal to 0.

$3^3- 3\times 3^2+ a\times 3 - 10 =0\\\Rightarrow 27 - 27 +3a-10=0\\\Rightarrow 3a = 10\\\Rightarrow \bold{a = \dfrac{10}{3}}$

So, the answer is:

$\bold{a = \dfrac{10}{3}}$

Answer 2

above answer is correct.....have a good day