Question

the sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, then find the equation​

Answer 1

Answer:

Let the roots be A and B.

» A + B = 5 & A³ + B³ = 35

» A³ + B³ = (A + B)³ - 3AB (A + B)

» 35 = 125 - 3AB (5)

» AB (5) = 30

» AB = 6

Therefore, the equation is

» x² - (A + B)x + AB = 0

» x² - 5x + 6 = 0

Answer 2

Answer:

let the roots be x and y

given,

x³ + y³ = 35

and

x +y = 5

on cubing both sides

(x +y)³ = 5³

=> x³ +y³ +3xy(x +y) = 125

=> 35 + 3xy* 5 = 125

=> 15xy = 125 - 35 = 90

=> xy = 90/15 = 6

now,

sum of roots = x +y = 5

and product of roots = xy = 6

we know,

the quadratic equation is given by →

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

=> x² -5x +6 =0

this is the required quadratic equation

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