Question

the quadratic polynomial whose sum and product of the zeroes are-3 and 5​

Answer 1

Given :

• Sum of zeroes = - 3
• Product of zeroes = 5

To Find :

• Quadratic Polynomial

Solution :

Let, α and β be zeroes of polynomial

• α + β = -3
• αβ = 5

Use formula for Quadratic equation :

⇒k[x² - (sum of zeroes)x + Product of zeroes]

⇒k[x² - (α + β)x + αβ]

⇒k[x² - (-3)x + 5]

⇒k[x² + 6x + 5]

⇒x² + 6x + 5

$\therefore$ Quadratic polynomial is x² + 6x + 5.

Answer 2

Solution :

It is given that,

the sum of zeroes = - 3/5

the product of zeroes = - 13/5

We know that,

sum of zeroes = - b/a

⇒ α + β = - 3/5

On comparing, b = 3 and a = 5

Also,

product of zeroes = c/a

⇒ αβ = c/a

⇒ αβ = - 13/5

On comparing, c = - 13 and a = 5

From this,

a = 5, b = 3 and c = - 13

We also know that, a quadratic equation is :- ax² + bx + c

Hence,

⇒ 5x² + 3x - 13 = 0

Hope it helps ❣️