Question

find the value of 'm' if (x-3) is factor of x²-mx-15​

Answer 1

Step-by-step explanation:

Given:

• (x-3) is factor of x^2 - mx - 15.

To find:

• Value of 'm' in the above expression = ?

Solution:

Let f(x) = x^2 - mx - 15 be any polynomial.

We know x - 3 is the factor of f(x). So, we can apply factor theorem to find 'm'.

First, we have to find the zero of this polynomial.

==> x - 3 = 0

==> x = 3

So, the zero of the polynomial is 3.

[put this value in f(x) and equate them with 0 to find 'm']

$= = > \: f(3) \: = \: {3}^{2} - \: m \times 3 \: - \: 15$

==> f(3) = 9 - 3m - 15 = 0

==> f(3) = -6 - 3m = 0

==> f(3) = -3m = 6

==> f(3) = m = 6/-3

==> m = -2

Hence, value of 'm' = -2

________________________________

Not sure? Let's verify !

(put the values again for verification)

If we get 0 as a result, it will be verified.

$= = > \: {3}^{2} - ( - 2 ) \: \times \: 3 \: - \: 15$

$= = > \: 9 \: + \: 6 \: - \: 15$

==> 15 - 15

==> 0

The value of 'm' is -2. Hence, verified ✔

Hope it helped you dear...