Question

the sum of two roots of quadratic equation is 1/2 and sum of their squares is 25/4 then find the quadratic equation ​

Answer 1

Answer:

2x² - x - 3

Step-by-step explanation:

To find----> Sum of two roots of quadratic equation is 1/2 and sum of their squares is 25/4 .

To find-----> Quadratic equation

Solution-----> Let α and β be the roots of equation ATQ,

Sum of roots = 1 / 2

=> α + β = 1 / 2

Sum of squares of root = 25 / 4

=> α² + β² = 25 / 4

We know that ,

( a + b )² = a² + b² + 2ab

Putting a = α and b = β , we get ,

( α + β )² = α² + β² + 2αβ

Putting α + β = 1 / 2 and α² + β² = 25 / 4

=> ( 1 / 2 )² = 25 / 4 + 2αβ

=> 1 / 4 = 25 / 4 + 2αβ

=> 1 / 4 - 25 / 4 = 2αβ

=> ( 1 - 25 ) / 4 = 2αβ

=> ( -24 ) / 4 = 2αβ

=> - 6 = 2αβ

=> αβ = - 6 / 2

=> αβ = - 3

Now required quadratic equation is ,

x² - ( α + β )x + αβ = 0

=> x² - ( 1/2 ) x + ( -3 ) = 0

=> 2x² - 2 ( 1 / 2 ) x - 3 = 0

=> 2x² - x - 3 = 0