172
Form a polynomial whose zeroes are $\alpha^2$ and $\beta^2$, where $\alpha$ and $\beta$ are zeroes of the polynomial $p(x) = x^2-3\sqrt{2}x+4$.
Show SolutionHide Solution↓
OR
(b) $\alpha+\beta= 3\sqrt{2}$, $\alpha\beta = 4$ (1/2+1/2 Mark)
alpha^2 +
beta^2 = (
alpha +
beta)^2 - 2
alpha
beta = 10$$\begin{aligned}& (1 Mark) \\ & alpha^2 \beta^2 = 4^2 = 16\end{aligned}$$ (1/2 Mark)
Required polynomial is $x^2 - 10x + 16$ or $k(x^2 - 10x + 16)$ where $k$ is a non zero real number. (1/2 Mark)
(b) $\alpha+\beta= 3\sqrt{2}$, $\alpha\beta = 4$ (1/2+1/2 Mark)
alpha^2 +
beta^2 = (
alpha +
beta)^2 - 2
alpha
beta = 10$$\begin{aligned}& (1 Mark) \\ & alpha^2 \beta^2 = 4^2 = 16\end{aligned}$$ (1/2 Mark)
Required polynomial is $x^2 - 10x + 16$ or $k(x^2 - 10x + 16)$ where $k$ is a non zero real number. (1/2 Mark)