Question

the sum of roots of quadratic equation is 5and sum of squares is 13.find the equation​

Answer 1

Solution :-

Let two Roots of Quadratic Equation are a & b .

Given That :-

→ a + b = 5

→ a² + b² = 13.

→ a + b = 5

Squaring both sides we get,

→ (a + b)² = 5²

→ a² + b² + 2ab = 25

putting value of a² + b² = 13 , we get,

→ 13 + 2ab = 25

→ 2ab = 25 - 13

→ 2ab = 12

→ ab = 6

So, we can say That, Sum of roots of Equation is 5 and Product of roots is 6.

Now,

we know That :-

→ Required Equation :- x² - (sum of Roots)x + Product of Roots = 0

putting values ,

→ Required Quadratic equation = x² - 5x + 6 = 0 (Ans).

Answer 2

Question :- the sum of roots of quadratic equation is 5and sum of squares is 13.find the equation ?

Solution :-

Let us assume that, two Roots of quadratic equation are x and y .

=> a + b = 5

Square both sides of the Equation

=> (a + b)² = 5²

=> a² + b² + 2ab = 25

putting value of a² + b² = 13

=> 13 + 2ab = 25

=> 2ab = 25 - 13

=> 2ab = 12

=> ab = 6 = Product of Roots .

Hence Required Equation :- x² - (sum of Roots)x + Product of Roots = 0

=> Required equation = x² - 5x + 6 = 0 .