Given:
Polynomial = P(x) = 3x² + kx + 6
Factor of the ablove polynomial = (x+3)
To Find:
Value of K, for which (x+3) become the factor of P(x) = 3x² + kx + 6
Solution :
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
V E R I F I C A T I O N :
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 !