Question

Sum of root of quadratic equation is 5 and sum of squares is 13 find the equstion

Answer 1

Solution :-

As given that

Sum of roots = 5

Sum of squares of roots = 13

Now As we have :-

a² + b² = (a+b)² - 2ab

Let the roots be α and β

Then

α² + β² = 13

→ (α+β)² - 2αβ = 13

→ (5)² - 2αβ = 13

→ 25 - 2αβ = 13

→ 2αβ = 25 - 13

→ 2αβ = 12

→αβ = 12 ÷ 2

→ αβ = 6

Now as we know that a quadratic equation is in the form of

k( x² - Sx + P )

Where

S = Sum of roots

P = Product of roots

k = constant term

So by replacing values Quadratic equation :-

= k( x² -(α+β)x + αβ)

= k(x² - 5x + 6 )

Now if k = 1 , Then our Quadratic Equation :-

= x² - 5x + 6