Question

The quadratic equation for which the sum of the roots is 7 and the sum of the squares of the roots is 25 is

Answer 1

Given,

Sum of roots of quadratic equation = 7

Sum of squares of roots = 25

To Find,

The quadratic equation

Solution,

Let the roots of the equation be x and y.

So,

x+y = 7

x²+y² = 25

(x+y)²-2xy = 25

49-25 = 2xy

24 = 2xy

xy = 12

Now, the formula of quadratic equation is

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

x²-7x+12

Hence, the quadratic equation is x²-7x+12.

Answer 2

Given; the sum of the roots is 7 and the sum of the squares of the roots is 25

To Find The quadratic equation

Solution It is given that some of the roots are 7 and the sum of the squares of the roots is 25

Sum of roots = 7

Sum of squares of roots =25

Let roots be x and y

(x + y)² = x² + y² + 2xy

49= 25+2xy

8=xy

So the product of roots =8

A quadratic equation is x² − Sx + P

x² − 7x + 8

Hence the quadratic equation is x² − 7x + 8