Question

Find a quadratic polynomial whose zeroes are -3 and 5

Answer 1

I hope it helps you

Answer 2

Answer:

$The \:quadratic \:polynomial \\\:will\: be\: x^{2}-2x-15.$

Step-by-step explanation:

$Let \: the \: quadratic\: polynomial \\\: be \: ax^{2}+bx+c, a≠0 \: and\\ \: its \: zeroes \: be \\\:\alpha \: and \: \beta$

$Here\: \alpha = -3 , \beta = 5$

$i )Sum\: of\: the\: zeroes \\= \alpha+\beta\\=-3+5\\=2$

$ii) Product \:of \:the \:zeroes \\= \alpha\beta \\=(-3) \times 5\\=-15$

Therefore,

$The \:quadratic \:polynomial\\\: ax^{2}+bx+c\: is\\ \:k[x^{2}-(\alpha+\beta)x+\alpha\beta],\\\: where\: k\: is\: a \:constant\\=k(x^{2}-2x-15)\:</p><p>\\We \:can \:put \:different\\ \:values \:of\: k.\\</p><p>When \:k \:= 1 ,$

$The \:quadratic \:polynomial \\\:will\: be\: x^{2}-2x-15.</p><p>$