<p>The cubic polynomial $\mathrm{g}\left( x \right)$ is such that the coefficient of ${{x}^{3}}$ is $3$ and the roots of the equation $\mathrm{g}\left( x \right)=0$ are $1$, $2$, and $k$. Given that&nbsp;$\mathrm{g}\left( x \right)$ has a remainder of $10$ when divided by $x-3$, show that&nbsp;$k=\frac{4}{3}$. Hence or otherwise, find the remainder when&nbsp;$\mathrm{g}\left( x \right)$ is divided by $3x-6$.</p>

The cubic polynomial $\mathrm{g}\left( x \right)$ is such that the coefficient of ${{x}^{3}}$ is $3$ and the roots of the equation $\mathrm{g}\left( x \right)=0$ are $1$, $2$, and $k$. Given that $\mathrm{g}\left( x \right)$ has a remainder of $10$ when divided by $x-3$, show that $k=\frac{4}{3}$. Hence or otherwise, find the remainder when $\mathrm{g}\left( x \right)$ is divided by $3x-6$.

Quadratic Functions - General

Quadratic Expressions, Equations, and Functions

Quadratic Expressions, Equations, and Functions - Quadratic Functions - General

Question 3dbb9a7c

Video Solution: