# Find the quadratic equation whose roots are at x = 3 and x = 5.

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

We need to determine the quadratic equation whose roots are 3 and 5.

There are two ways to find the equation.

We will use the factors method to determine  the function.

We find the factors of the quadratic function.

Let f(x) be the function where 3 and 5 are the roots.

==> Then, the factors are (x-3) and (x-5)

==> f(x) = (x-3)(x-5)

We will open the brackets.

==> f(x) = x^2 -3x -5x + 15

==> f(x) = x^2 - 8x + 15

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The roots of the quadratic equation are x= 3 and x = 5

So we can write: (x - 3)(x - 5) = 0

=> x^2 - 3x - 5x + 15 = 0

=> x^2 - 8x + 15 = 0

The required quadratic equation is x^2 - 8x + 15 = 0

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The quadratic equation whose roots are x= x1 and x= x2 is (x-x1)(x-x2) = 0. Or x^2 -(x1+x2)x+x1x2 = 0.

So the quadratic equation whose roots are x= 3 and x = 5 is obtained by the product (x-3)(x-5) = 0.

=> x(x-5) -3(x-5) = 0

=> x^2-5x-3x + 3*5 = 0.

=> x^2-(3+5)x+ 3*5 = 0.

=> x^2-8x +15 = 0.

Therefore the quadratic equaltion is x^2-8x+15 = 0