I worked out that the roots of this
3x^2 -3

are x=1 or x=-1 is this correct?
my classmate said he got x=-1 or x=1.7

2. Originally Posted by wolfhound
I worked out that the roots of this
3x^2 -3

are x=1 or x=-1 is this correct?
my classmate said he got x=-1 or x=1.7
if you mean ...

$3x^2-3=0$

then the roots are $x = \pm 1$

3. You are correct.

You have $3x^2 - 3 = 0$

Divide both sides by 3

$=> x^2 - 1 = 0$

Move the one to the right hand side

$=> x^2 = 1$ and so $x = \sqrt{1} = 1 \textrm{ or } -1$

4. Originally Posted by wolfhound
I worked out that the roots of this
3x^2 -3

are x=1 or x=-1 is this correct?
my classmate said he got x=-1 or x=1.7
You should suggest to your classmate that s/he substitute x = 1.7 into the equation and see what happens ....

5. There is something of an ambiguity about the term "roots". I learned that an equation has roots while a polynomial has zeros. Specifically, the zeros of the polynomial p(x) are the roots of the equation p(x)= 0. Strictly speaking, then, you can talk about the "roots" of the equation $3x^2- 3= 0$, or the "zeros" of the polynomial $3x^2- 3$. But students tend to use "root" and "zero" interchangebly. In either case, since $3x^2- 3= 0$ is the same as $3x^2= 3$ and, dividing both sides by 3, $x^2= 1$, the roots are indeed x= 1 and x= -1. As mr fantastic suggested, have your friend replace x in the equation by 1.7 and see what happens. He should get approximately "6", not "0".

6. Originally Posted by HallsofIvy
There is something of an ambiguity about the term "roots". I learned that an equation has roots while a polynomial has zeros. Specifically, the zeros of the polynomial p(x) are the roots of the equation p(x)= 0. Strictly speaking, then, you can talk about the "roots" of the equation $3x^2- 3= 0$, or the "zeros" of the polynomial $3x^2- 3$. But students tend to use "root" and "zero" interchangebly. In either case, since $3x^2- 3= 0$ is the same as $3x^2= 3$ and, dividing both sides by 3, $x^2= 1$, the roots are indeed x= 1 and x= -1. As mr fantastic suggested, have your friend replace x in the equation by 1.7 and see what happens. He should get approximately "6", not "0".
I was wondering about that. Thanks for the info