Question

If α, β are zeroes of the polynomial x2-2x-8, then form a quadratic polynomial whose zeroes are 2α and 2β

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$Form\: of \: a\: polynomial\\whose \: zeroes \: are\: 2\alpha \: and\: 2\beta\\ \: is \: x^{2}-4x-32$

Step-by-step explanation:

$Given \: \alpha \: and \: \beta\\ are \: two \: zeroes \: of\\ the \: polynomial \: x^{2}-2x-8$

$Sum \: of \:the \: zeroes \\=\alpha + \beta\\=-\frac{x-coefficient }{x^2-coefficient}\\=-\frac{-2}{1}\\=2---(1)$

$Product\:of \: the \: zeroes\\=\alpha \beta\\=\frac{constant}{x^{2}\: coefficient}\\=\frac{-8}{1}\\=-8---(2)$

$Now,\\If\: Zeroes\:of \: polynomial\\ \: are \:2\alpha \: and \: 2\beta$

$Form\: of \: a\: polynomial:\\x^{2}-(sum\:of\:the \:zeroes )x+product\:of\:zeroes$

$x^{2}-(2\alfa+2\beta)x+(2\alfa\times 2\beta$

$=x^{2}-2(\alpha+\beta)+4\alpha\beta$

$=x^{2}-2\times 2x+4(-8)$

/* From (1) and (2) */

$= x^{2}-4x-32$

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