Question

Find a quadratic polynomial , the sum and the product of whose zeroes are -3 and 2 , respectively.

Explain your answer briefly !!

Thanks :)

Answer 1

Answer:

the quadratic polynomial will be x²+x-6.

Step-by-step explanation:

Let the quadratic polynomial be

ax²+bx+c, a≠0 and it's zeroes be $\alpha \:and \:\beta$

$Here, \alpha = -3 ,\: \beta = 2$

$Sum \:of \:the \: zeroes \\=\alpha+\beta = -3+2=-1$

$Product \:of \:the \: zeroes \\=\alpha \beta = (-3)\times 2=-6$

Therefore,

The quadratic polynomial is

$k[x^{2}-(\alpha+\beta)x+\alpha \beta ], \\where \:k \:is \:a \: constant$

$= k[x^{2}-(-1)x+(-6)]$

$=k(x^{2}+x-6)$

We put different values of k.

when k=1 ,

the quadratic polynomial will be x²+x-6.

•••♪