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Form a polynomial whose zeroes are $\alpha^2$ and $\beta^2$, where $\alpha$ and $\beta$ are zeroes of the polynomial $p(x) = x^2-3\sqrt{2}x+4$.
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$\alpha+\beta= 3\sqrt{2}$, $\alpha\beta = 4$ (1/2+1/2 Mark)
α² + β² = (α + β)² - 2αβ = 10 (1 Mark)
α² β² = 4² = 16 (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)
α² + β² = (α + β)² - 2αβ = 10 (1 Mark)
α² β² = 4² = 16 (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)