Question

Find the value of m, if (x + 3) is a factor of
$3{x}^{2} + mx + 6$
​

Answer 1

Given

Eq:- 3x² + mx + 6

(x + 3) is a factor

Now

f(x) = x + 3

We know that

f(x) = 0

x + 3 = 0

x = -3

let

p(x) = 3x² + mx + 6

We know that

p(x)= 0

3x² + mx + 6 = 0

Now put the value of x = -3

3x² + mx + 6 = 0

where x = -3

3(-3)² + m(-3) + 6 = 0

3×9 - 3m + 6 = 0

27 - 3m + 6 = 0

33 = 3m

m = 33/3

m = 11

So Value of m = 11

Now Check our Answer

3x² + mx + 6 = 0

where m = 11 and x = -3

3(-3)² + 11(-3) + 6 = 0

3×9 - 3×11 + 6 = 0

27 - 33 + 6 = 0

33 - 33 = 0

0 = 0

LHS = RHS