What is the sum of the roots of the equation ax^2 + bx + c = 0?

Question

please no answeres like, i dont know.

What is the product of its roots?

Answer 1

sum: -b/a
product: c/a


d:

Answer 2

The quadratic formula tells you the roots of an equation of this form. The two roots can be written as:

x = -b/(2*a) +/- sqrt(b^2 - 4*a*c)/(2*a)

One root uses the + from the +/-, the other uses the -. If you add the two roots together, the + and - from each root will cancel, leaving you with:

x1 + x2 = -b/a

Multiplying the two roots yields:

x1 * x2 = c/a

Answer 3

sum of the root = - b/a
product of roots = c/a

to understand this, consider the following example
(x - α)*(x - ß) = 0
this equation has roots x = α and x = ß

now (x - α)*(x - ß) = x² - ßx -αx + αß = x² - (α+ß) x + αß = 0

we can write ax^2 + bx + c = 0 in same form
note ax² + bx + c = a(x² + (b/a) x + (c/a)) = 0
=> x² + (b/a) x + (c/a) = 0

compare this with x² - (α+ß) x + αß = 0

Answer 4

you know the quadratic formula yields the equations for the roots.
root1) 1/2/a*(-b+(b^2-4*a*c)^(1/2))
root2) 1/2/a*(-b-(b^2-4*a*c)^(1/2))

The product is
1/4/a^2*(-b+(b^2-4*a*c)^(1/2))*(-b-(b^2-4*a*c)^(1/2))

which simplifies to
c/a

Answer 5

0 LOL!