Question

Example-5. Find the quadratic polynomial, whose sum and product of the zeroes are - 3 and
2, respectively.​

Answer 1

Step-by-step explanation:

${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ {x}^{2} + 3x + 2 = 0$

Answer 2

Let the quadratic polynomial be

${ax}^{2} + bx + c$

And zeroes be

$\alpha \: and \: \beta .$

We have

$\alpha + \beta = - 3 = \frac{ - b}{a}$

And

$\alpha \beta = 2 = \frac{c}{a}$

If we take a=1 , then b=3 and c= 2

$so$

So,one quadratic polynomial which fits the given conditions is =

${x}^{2} + 3x + 2$

Similarly,we can take 'a' to be any real number.Let us say it is K.

This gives

$\frac{ - b}{k} = - 3 \: or \: b = 3k \: and \: \frac{c}{k} = 2 \: or \: c = 2k.$

Substituting the value of a,b and c ,we get the polynomial =

${kx}^{2} + 3kr + 2k$

☠︎Ok bro ☠︎