Find the value of k, if (x+3) is a factor of 3x²+kx+6 Question Find the value of k, if (x+3) is a factor of 3x²+kx+6 in progress 0 Math Arianna 3 months 2021-10-15T17:17:56+00:00 2021-10-15T17:17:56+00:00 2 Answers 0 views 0

## Answers ( )

Given:Polynomial = P(x) = 3x² + kx + 6

Factor of the ablove polynomial = (x+3)

To be found:Value of K, for which (x+3) become the factor of P(x) = 3x² + kx + 6

Now,

x + 3 = 0

⇒ x = (-3)

So,

As (x+3) is a factor so x = (-3) is one root of the polynomial.

Therefore,

P(-3) = 0

→ P(-3) = 3(-3)² + k(-3) + 6 = 0

→ 3(9) – 3k + 6 = 0

→ 27 – 3k + 6 = 0

→ 27 + 6 – 3k = 0

→ 33 – 3k = 0

→ – 3k = -33

→ k = -33 ÷ -3

→ k = 11

Hence,

For the value of k = 11, (x+3) is a factor of 3x²+ kx + 6

Verification:3x²+ kx + 6, by putting the value of k = 11 and taking -3 as root the remainder should be zero

= 3x²+ 11x + 6

= 3(-3)² + 11(-3) + 6

= 3(9) – 33 + 6

= 27 – 33 + 6

= 27 + 6 – 33

= 33 – 33

= 0

Hence verified.