Question

if a+B=5 and a³+B³=35 find the quadratic equation whose roots are a and B​

Answer 1

Step-by-step explanation:

Given,

α+β = 5 and,

α³+β³ = 35

(a+b)³ = a³+b³+3ab(a+b)

Here, a=α and b=β

(α+β)³ = α³+β³+3αβ(α+β)

Entering the given values, we get

(5)³ = 35 + 3αβ(5)

125 = 35 + 3αβ(5)

90 = 3αβ(5)

αβ = 6

The quadratic equation is given by

⇒ x²-(α+β)x+αβ

∴ x²-5x+6