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

hala718 | Certified Educator

calendarEducator since 2008

starTop subjects are Math, Science, and Social Sciences

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...

(The entire section contains 2 answers and 116 words.)

check Approved by eNotes Editorial

## Related Questions

justaguide | Certified Educator

calendarEducator since 2010

starTop subjects are Math, Science, and Business

check Approved by eNotes Editorial

neela | Student

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

check Approved by eNotes Editorial