SOLUTION: Write a quadratic equation such that the sum of its roots is 6 and the product of its roots is -27.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Write a quadratic equation such that the sum of its roots is 6 and the product of its roots is -27.       Log On


   

Question 941191: Write a quadratic equation such that the sum of its roots is 6 and the product of its roots is -27.
Found 2 solutions by richard1234, stanbon:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 - 6x - 27 = 0

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Write a quadratic equation such that the sum of its roots is 6 and the product of its roots is -27.
-----
Since the roots are [-b+sqrt(b^2-4ac)]/2a and [-b-sqrt(b^2-4ac)]/(2a)
------
Sum of the roots is 2[-b/(2a)] = -b/a
-----
Product is (b^2-(b^2-4ac)]/(4a^2) = 4ac/4a^2 = c/a
--------
Equation:
y = x^2 - (sum of roots)x + (product of roots)
-----
y = x^2 -6x -27
===================
Cheers,
Stan H.
===================