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.. (Worried) So anyone please help me what I've done wrong...

This is what i've done
Attachment 29930



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)

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.

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

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).

There are 4 choices for digits for $\displaystyle a$ (since $\displaystyle a \neq 0$). That leaves 4 digits for $\displaystyle b$. Once you choose that, there are 3 digits left for $\displaystyle c$. 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?