Question

9.* The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find
the equation.​

Answer 1

ANSWER:

• The equation is x² - 5x + 6 = 0.

GIVEN:

• The sum of two roots of a quadratic equation is 5

• sum of their cubes is 35.

TO FIND:

• The equation.

EXPLANATON:

Let the roots be x and y

x + y = 5

x³ + y³ = 35

x³ + y³ = (x + y)(x² - xy + y²)

35 = 5( x² - xy + y²)

x² + y² = (x + y)² - 2xy

7 = (x + y)² - 2xy - xy

7 = 5² - 3xy

7 - 25 = - 3xy

- 18 = - 3xy

xy = 6

Quadratic equation = x² - (sum of roots)x + product of roots

sum of roots = 5

product of roots = 6

The equation = x² - 5x + 6 = 0.