Question

Find the quadratic polynomial such that the sum of zeros is zero and the product of zeros is - root 5/2

Answer 1

Given:

sum of zeros is zero and

the product of zeros is - root 5/2

To find:

the quadratic polynomial  which suits the condition.

Pre-requisite Knowledge:

Standard form of quadratic equation = ax² + bx + c = 0

If α and β are the zeros of the polynomial then,

α + β = -b/a

α * β = c/a

Solving Question:

We are given the sum and product of  zeros of the polynomial.We could substitute the values in above formulas to find the answer.

Solution:

α + β = 0 [Given]

⇒ 0/2 = -b/a

⇒ a = 2 ; b = 0

α * β = -√5/2 [Given]

⇒ -√5/2 = c/a

⇒ c = -√5

∴ The quadratic polynomial is k[2x² - √5 = 0 ] , where 'k' is a constant.

Answer 2

$\huge{\boxed{\mathtt{\purple{Answer}}}}$

The quadratic polynomial is k[2x² - √5 = 0 ] , where 'k' is a constant.
Given:
sum of zeros is zero and
the product of zeros is - root 5/2
To find:
the quadratic polynomial which suits the condition.
Pre-requisite Knowledge:
Standard form of quadratic equation = ax² + bx + c = 0
If α and β are the zeros of the polynomial then,
α + β = -b/a
α * β = c/a
Solving Question:
We are given the sum and product of zeros of the polynomial.We could substitute the values in above formulas to find the answer.
Solution:
α + β = 0 [Given]
⇒ 0/2 = -b/a
⇒ a = 2 ; b = 0
α * β = -√5/2 [Given]
⇒ -√5/2 = c/a
⇒ c = -√5
∴ The quadratic polynomial is k[2x² - √5 = 0 ] , where 'k' is a constant.