Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have problems every time I face a quadratic equation. What can I do to learn how to solve them? Can anyone please show me how to solve the one below and explain the basic principle of solving quadratic equations.

$$x^2- xa - ab = 0$$

share|improve this question
add comment

2 Answers

up vote 4 down vote accepted

There is a formula: $$Ax^2 + Bx + C = 0 \quad \Rightarrow \quad x_{1,2} = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A}.$$ $A$ is whatever is next to $x^2$, $B$ is whatever is next to $x$, and $C$ is without $x$. In your case: $$x^2 - xa - ab = 1 \cdot x^2 + (-a)x + (-ab) = 0 \quad \Rightarrow \quad A = 1, \quad B = -a, \quad C = -ab,$$ so $$x_{1,2} = \frac{a \pm \sqrt{a^2 + 4ab}}{2}.$$

share|improve this answer
    
Where does this formula come from? –  71GA Jul 15 '13 at 15:09
1  
It's a well known formula which you can easily check by substituting $x_1$ and $x_2$ for $x$. @JamesMaslek has just give the proper link, so I won't repeat what he wrote. –  Vedran Šego Jul 15 '13 at 15:15
    
the formula is actually derived in a different question on this site –  Zar Jul 15 '13 at 15:17
2  
Here is the question @Zar is talking about: math.stackexchange.com/questions/49229/… –  Josué Molina Jul 15 '13 at 15:37
add comment

The solution to any quadratic is the well known Quadratic Formula.

$x = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A}$ (as @Vedran Sego has). This comes from completing the square

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.