# Math Help - Finding Quadratic equation Possible if the coefficient is known

1. ## Finding Quadratic equation Possible if the coefficient is known

So, the question is :

If 3 different numbers are taken from the set {0,1,3,5,7} to be used as the coefficient of a standard quadratic equation

a) How many such quadratic equations can be formed?
b) How many of these have real roots
I have work on it, but the result is different from the answer key.. So anyone please help me what I've done wrong...

This is what i've done

and I got 60+12+12 = 84 equations for (a) and 18 equations for (b)
but the book says it should be 88 for (a) and 28 for (b)

2. ## Re: Finding Quadratic equation Possible if the coefficient is known

Hey Deci.

Hint: Remember that you can use 0 for the x term coefficients as well as the final coefficient (c value). I don't think you factored this in.

3. ## Re: Finding Quadratic equation Possible if the coefficient is known

Thanks for the hint chiro,,
but it says 3 different numbers, so 0 shouldn't be repeated, isn't it?

4. ## Re: Finding Quadratic equation Possible if the coefficient is known

What I mean is that zero can be used for b or x in ax^2 + bx + c = 0. From your post I got the feeling that you didn't take into account that b could be zero (as well as c).

5. ## Re: Finding Quadratic equation Possible if the coefficient is known

There are 4 choices for digits for $a$ (since $a \neq 0$). That leaves 4 digits for $b$. Once you choose that, there are 3 digits left for $c$. So, there are 4*4*3=48 quadratic equations, which is much fewer than the 88 the book counted. Are you sure the digits should be different?