Question

Find the value of $k$, if $x-1$ is factor of $P\left(x\right)$ and $P\left(x\right)=3x^2+kx+\sqrt{2}$

• A. $-2-\sqrt{2}$
• B. $-3-\sqrt{2}$
• C. $3-\sqrt{2}$
• D. None of these

Answer 1

Answer: (B)

$-3-\sqrt{2}$

$(x-1)$ is a factor of

$P\left(x\right)=3x^2+kx-\sqrt{2}$

$\therefore$By remainder theorem,

$x-1=0$

$\therefore x=1$

$\therefore P\left(1\right)$ must be equal to $0$

$\therefore P\left(1\right)=3{\left(1\right)}^2+k\left(1\right)+\sqrt{2}$

$\therefore P\left(1\right)=3+\sqrt{2}+k=0$

$\therefore k=-3-\sqrt{2}$