# What are the roots of the quadratic equation if the sum is 5 and the product is 6 ?

Let f(x) = ax^2 + bx + c   is a quadratic function such that x1 and x2 are the roots.

==> Given that:

x1 + x2 = 5

x1*x2 = 6

But we know that:

x1+ x2 = -b/a = 5 ==> b= -5 a

Also, we know that:

x1*x2 = c/a = 6 ==> c = 6 a

==> f(x) = ax^2 -5a x + 6a

We need to find the roots.

==> ax^2 - 5a x + 6 a = 0

We will divide by a:

==> x^2 -5x + 6 = 0

==> (x -2)(x-3) = 0

Then, the roots are : x = { 2, 3}

Approved by eNotes Editorial Team

We have the sum of the roots of the quadratic equation as 5 and the product of the roots as 6.

Let the roots be A and B. Here we don't need to consider the quadratic equation. We can find A and B just by using the fact that A*x2 = 6 and A + B = 5

A + B = 5

=> A = 5 - B

substituting this in A*B = 6

=> B*( 5 - B) = 6

=> 5*B - B^2 = 6

=> B^2 - 5B + 6 = 0

=> B^2 - 3B - 2B + 6 =0

=> B(B - 3) - 2(B -3) = 0

=> (B - 2)(B -3) =0

B = 2 and  3

A = 3 and 2

The required roots are 2 and 3.

Approved by eNotes Editorial Team