Little confusing i'm not sure, how bout u?

[aisha]

Here is the question 3x^2-24x+48=0, determine the value of the discriminant. What does this value tell you about the equation? How many times does the corresponding function cross the x-axis?

Ok first part a=3 b=-24 c=48
discriminant b^2-4ac
so (-24)^2-4(3)(48)
576-576=0

So first question what does the value tell u about the equation? Would it be right to say that the value 0 tells us that the equation has one double root?

And for the second question? Well would it be right to say that the function doesn't cross the axis at all? Or well it could have crossed twice if the double root was negative, but if its a root then it can't be in the middle it must be on the x-axis?

LITTLE CONFUSED PLZ HELP ME OUT

 

[Gokul43201]

Correct on the first part...not on the second.

A quadratic is basically a parabola. The roots are where the parabola touches/intersects the x-axis. If there's only one root, what does this mean ?

 

[cepheid]

Ok first part a=3 b=-24 c=48
discriminant b^2-4ac
so 144-4(3)(-12) this = 144-144=0

Um...hmmmm...what is going on here?
a = 3, b = -24, c = 48

Well, you got that part right, so why didn't you substitute those values into the expression for the discriminant?

$$b^2 - 4ac$$

$$= (-24)^2 - 4(3)(48)$$

$$= 576 - 576 = 0$$

Yeah okay, so it still turns out to be zero, but that's from luck more than anything else. In your expression, it's as though b suddenly became 12, and c suddenly became -12. Where do these numbers come from?

You can divide everything by 3 to get

a = 1, b = -8, c = 16, and of course you get the same answer.

 

[aisha]

Oh sorry you are right I did mess up the numbers lol I fixed them but still need help in answering the 2 questions. I know the value of the discriminant is 0 but?

What does this value tell about the equation?
I think it tells that the equation has one real double root.

How many times does the corresponding function cross the x-axis?
Im not sure? Help someone?

 

[hypermorphism]

I know the value of the discriminant is 0 but?

What does this value tell about the equation?
I think it tells that the equation has one real double root.

How many times does the corresponding function cross the x-axis?

See what role the discriminant plays in the quadratic formula (the general solution of a quadratic equation):
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
What happens when the discriminant is less than zero ? What does this imply about the graph of the function $$f(x) = ax^2 + bx + c$$ (Specifically, does it ever cross the x-axis) ?
Similarly, what happens to the graph when the discriminant is positive ? When it is exactly zero (You will find you are right in that it represents a double root, as the formula becomes
$$x = \frac{-b \pm \sqrt{0}}{2a}$$

 

[aisha]

I still don't know is this function crossing the x-axis?

 

[hypermorphism]

I still don't know is this function crossing the x-axis?

If a parabola has a double root, that means the vertex touches the x-axis, since any other configuration of the vertical parabola either does not touch the axis (no roots) or crosses the axis (two distinct roots).

 

[Jameson]

It has one root, since the discriminant doesn't change the other part of the equation.

hypermorphism explained it

 

[aisha]

Thanks you guys I got it finally lol