The value of ‘K’ for which 2x4 + 3x3 + 2Kx2 + 3x + 6 is exactly d

1.	The value of ‘K’ for which 2x4 + 3x3 + 2Kx2 + 3x + 6 is exactly divisible by x + 2?A) 1 B) -1 C) 2 D) -2
Answer» Correct option is (B) -1 x+2 is a factor of \(2x^4+3x^3+2Kx^2+3x+6\) \(\therefore\) x = -2 is a root of equation \(2x^4+3x^3+2Kx^2+3x+6=0\) \(\therefore2(-2)^4+3(-2)^3+2k(-2)^2+3(-2)+6=0\) \(\Rightarrow\) 32 - 24 + 8k - 6 + 6 = 0 \(\Rightarrow\) 8k = -32+24 = -8 \(\Rightarrow\) \(k=\frac{-8}8=-1\) Correct option is B) -1

The value of ‘K’ for which 2x4 + 3x3 + 2Kx2 + 3x + 6 is exactly divisible by x + 2?A) 1 B) -1 C) 2 D) -2

Answer»

Correct option is (B) -1

x+2 is a factor of \(2x^4+3x^3+2Kx^2+3x+6\)

\(\therefore\) x = -2 is a root of equation \(2x^4+3x^3+2Kx^2+3x+6=0\)

\(\therefore2(-2)^4+3(-2)^3+2k(-2)^2+3(-2)+6=0\)

\(\Rightarrow\) 32 - 24 + 8k - 6 + 6 = 0

\(\Rightarrow\) 8k = -32+24 = -8

\(\Rightarrow\) \(k=\frac{-8}8=-1\)

Correct option is B) -1