Question

find the quadratic polynomial sum of whose zeros is 8 and their product is 12 hence find the zeros of the polynomial

Answer 1

The polynomial can be x^2 - 8x + 12. It's zeros are 6 and 2.

Answer 2

Sum=8
Product=12
polynomial=x square-(sum)x +product
=x square-8x+12
$\alpha + \beta = - b \div a$
So
Note- take the values of a and b from the polynomial.




$\alpha + \beta = 8 \div 1$

So,
$\alpha + \beta = 8$

$\alpha \times \beta = 12$
$\beta = 12 \div \alpha$
Substitute the value of beta for the sum
$\alpha + \beta = 8$
$\alpha + 12 \div \alpha = 8$
${ \alpha { }^{2} + 12} \div \alpha = 8$
$\alpha ^{2} - 8 \alpha + 12 = 0$
$\alpha = 6and 2$
Therefore,
$\alpha = 6$
$\beta = 2$
The zeroes are 6 and 2