Thinking

[pale wigeon]

if a or b or c is a fraction in ax^2 + bx + c, does that also mean the x-intercepts are fractions or can they be whole numbers.

[lone summit]

a is a fraction

x-intercepts are whole numbers

heres another example

[pale wigeon]

I was just thinking, wouldn't having a fraction as a b or c make it unfactorable and you'd have to use the quadratic formula? Where x never = a whole number/

?

[pale wigeon]

?

[peak valve]

he's shown u an example of when the coefficients are a fraction but the roots are not, try using the quadratic formula on 0.5x^2-4x+0 and see what happens. You can have fractional or integer roots with either integer or fractional coefficients

[loud vector]

I can show you another way to see this problem.

There are these things called Viéte-formulas

they say that in a quadratic ax^2+bx+c=0 there are two equations always ture

-b/a = x_1 + x_2 and c/a = x_1*x_2

Consider these two equations and you can see that there are infinitely many cases where a can be a fraction and x_1 and x_2 are integers

On the factorisation

you have to pull out the coefficient of the highest order term and proceed after that

eg

0.5x^2+4x = 0.5(x^2 + 8x)

Now you can factorize and you are going to have a 0.5 term at the beginning