Question

the third zero of the polynomial ,if the sum and product of whose zeroes are -3 and 2 is

Answer 1

Answer:

Pls refer the attatchment

Answer 2

Given: The sum of the zeroes is -3

            product is 2

To Find: The third zero of the polynomial

Solution: We assume our zeros of the polynomial as $\alpha\ and\ \beta$

$\alpha +\beta =-3\\and\ \alpha \beta =2$

We know, the polynomial is:-

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

 By Substituting the values we get,

$x^{2} + 3x + 2 = 0$

By splitting the middle term method we can find the zeroes of the polynomial,

$x^{2} + 2x + x + 2 = 0\\x ( x + 2 ) +1 ( x + 2 ) = 0\\( x + 1 ) ( x + 2 ) = 0$

So zeros are $\alpha =-1 \ and\ \beta =-2$

Answer:- So zeros are $\alpha =-1 \ and\ \beta =-2$