# Homework Help: Find the values of a

1. Jun 12, 2013

### utkarshakash

1. The problem statement, all variables and given/known data
The real values of a for which the equation x^2-3x+a=0 has three real and distinct roots is

3. The attempt at a solution
I started by writing the sign scheme of f'(x). But it is of no help to me. It will merely tell me the intervals in which f(x) increases or decreases. Also, if there are three distinct roots of f(x) then there must be two extrema.

2. Jun 12, 2013

### CAF123

Did you write down the problem statement correctly? If a is a real constant, then the equation x2 -3x + a = 0 gives the roots of a quadratic, which by the FTOA, there is exactly 2 roots in $\mathbb{C}$. Did you mean to write 'two real and distinct roots?

3. Jun 12, 2013

### utkarshakash

I'm really sorry. It is x^3.

4. Jun 13, 2013

### Staff: Mentor

Sketch the plot - for three distinct roots the extremes must be on both sides of the abscissa. And "a" changes position of the plot with regard to abscissa, so for some values you will have just one root, for some values two roots, and for some values three roots. Think how these things change depending on the number of extreme values and how the number of extreme values depend on "a".

5. Jun 13, 2013

### CAF123

You could try finding what values of a are roots of that function. That will allow you to factor out an (x±a) and you are automatically left with a simple quadratic