Question

a quadratic polynomial whose zeroes are 7and5​

Answer 1

Answer:

answer for the given problem

Answer 2

SOLUTION:-

Let zeroes of Quadratic polynomial be α and β.

•°• α = 7 and β = 5

now,

α + β = 7 + 5 = 12

And

α β = 7 × 5 = 35

Quadratic equation => x² - (α + β)x + αβ = 0

•°• => x² - (12)x + 35 = 0

•°• => x² - 12x + 35 = 0

Quadratic polynomial is x² - 12x + 35 = 0.

More Information:-

To obtain a quadratic equation having given roots.

Let α and β be the roots quadratic equation in variable x.

•°• x = α or x = β

•°• x - α = 0 or x - β = 0

•°• (x - α) (x - β) = 0

•°• x² - (α + β)x + αβ = 0

When two roots of equation are given the quadratic equation can be obtained as

x² - ( addition of roots )x + product of roots = 0