Question

Quadratic equations whose roots are 5,
3

Answer 1

ANSWER:

• Required quadrtic equation = x²-8x+15

GIVEN:

• First zero = 5
• Second zero = 3.

TO FIND:

• A quadrtic polynomial whose roots are 5 and 3.

SOLUTION:

Standard form of Quadratic polynomial when Zeros are given:

= x²-(α+β)x+αβ

Finding sum of zeros (α+β)

= 5+3

= 8

Here, (α+β) = 8

Finding product of zeros (αβ)

= 5(3)

= 15

Here, αβ = 15

Putting the values in the formula :

=> x²-8x+15 = 0

Required quadrtic equation = x²-8x+15

NOTE:

Some important formulas:

=> Sum of zeroes (α+β) = -(Coefficient of x)/Coefficient of x²

=> Product of zeroes (αβ) = Constant term/ Coefficient of x²