Roots & Product of ax^2 + bx + c = 0

In summary, the sum of the roots of the equation ax^2 + bx + c = 0 is -b/a and the product of the roots is c/a. This can be proven by factoring the equation and comparing corresponding coefficients. It is not necessary to know the specific values of the roots, as long as they are represented by r and s.
  • #1
rhule009
9
0
Prove that the sum of the roots and product of the roots of the equation
ax^2 + bx + c = 0 are
-b/a and c/a respectively
thank you
 
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  • #2
Do you know what the quadratic formula is?
 
  • #3
You don't need that. You dont' need to know what the roots are at all. You can let them be r and s, and just use standard results such as if r is a root of f(x), then f(x) = (x-r)g(x) for some g(x). I.e. just factorize the equation.
 
  • #4
If u and v are roots of that equation then
[tex]ax^2+ bx+ c= a(x- u)(x- v)[/itex]
Multiply the right side and compare corresponding coefficients.
 

Related to Roots & Product of ax^2 + bx + c = 0

1. What is the quadratic formula?

The quadratic formula is a mathematical formula used to solve quadratic equations in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The formula is x = (-b ± √(b^2 - 4ac)) / 2a.

2. How do you find the roots of a quadratic equation?

The roots of a quadratic equation can be found by using the quadratic formula or by factoring the equation. To factor, you need to find two numbers that when multiplied together, equal c, and when added or subtracted, equal b. These numbers will then be used as the roots of the equation.

3. What does the discriminant tell us about a quadratic equation?

The discriminant, b^2 - 4ac, of a quadratic equation can tell us the nature of the roots. If the discriminant is positive, there are two real and distinct roots. If it is zero, there is one real root. And if it is negative, there are no real roots, meaning the solution will involve imaginary numbers.

4. Can a quadratic equation have more than two roots?

No, a quadratic equation can only have a maximum of two roots, as it is a second-degree polynomial. This means that the highest exponent of the variable is 2, and therefore, there can only be two solutions.

5. How can the roots of a quadratic equation be interpreted in real-life situations?

The roots of a quadratic equation can represent the x-intercepts or solutions to a real-life problem. For example, if the equation represents the trajectory of a projectile, the roots would indicate the points where the projectile hits the ground.

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