Question

If the product of zeros of polynomial αx2-6x-6 is 4, find the value of α also find sum of the zeros of polynomial

Answer 1

Answer:

The sum of zeros is -4

value of   α is -3/2

Given:

• product of zeros of polynomial is 4

• polynomial  αx²-6x-6

To find:

• the value of α

• sum of the zeros of polynomial

Solving Question:

We are given the  product of zeros of polynomial is 4 and are asked to find its zeros as well the sum of zeros.We can find it using the relationship between zeros and coefficients.

If α and β are the zeros then,

α + β = -b/a

α * β = c/a

Solution:

αx²-6x-6

product of zeros of polynomial is 4

⇒ α * β = c/a

⇒ α * β = c/a = -6/a

or, -6/a = 4

or, a = -6/4

or, a = -3/2

value of   α is -3/2

Then, to find the sum of zeros

α + β = -b/a

α + β =  -(-6)/ -3/2

⇒ 6 * 2 / -3

or, 12/ -3

or, -4

∴ The sum of zeros is -4