Question

write the sum and product of the zeros of the polynomial 6x²-5x-7

Answer 1

the ans is given in pic

Answer 2

Given:

Polynomial P(x) = 6x²- 5x - 7

To Find:

What is the sum and product of the zeros of the polynomial 6x²- 5x - 7 ?

Solution:

From standard quadratic polynomial:

P(x) = a x² + b x + c     ...1)

Let above polynomial have zeroes α and β. There are relation between zeroes:

$\mathbf{\alpha +\beta =\dfrac{-b}{a}}$        ...2)

$\mathbf{\alpha \times \beta =\dfrac{c}{a}}$            ...3)

From given polynomial:

P(x) = 6 x² -5 x -7     ...2)

On comparing equation 1) and equation 2), we get:

a = 6    

b = -5

c = -7

Then sum and product of the zeros of the polynomial 6x²-5x-7 are find out by equation 2) and equation 3):

$\mathbf{Sum\ of\ zeroes\ (\alpha +\beta) =\dfrac{-(-5)}{6}=\dfrac{5}{6}}$

$\mathbf{Product\ of\ zeroes\ (\alpha \times \beta) =\dfrac{-7}{6}= - \dfrac{7}{6}}$