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

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- Nov 27th 2009, 01:31 PMwolfhoundquadratic roots
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 - Nov 27th 2009, 01:33 PMskeeter
- Nov 27th 2009, 01:36 PMDeadstar
You are correct.

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

Divide both sides by 3

$\displaystyle => x^2 - 1 = 0$

Move the one to the right hand side

$\displaystyle => x^2 = 1$ and so $\displaystyle x = \sqrt{1} = 1 \textrm{ or } -1$ - Nov 27th 2009, 04:28 PMmr fantastic
- Nov 27th 2009, 06:12 PMHallsofIvy
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 $\displaystyle 3x^2- 3= 0$, or the "zeros" of the polynomial $\displaystyle 3x^2- 3$. But students tend to use "root" and "zero" interchangebly. In either case, since $\displaystyle 3x^2- 3= 0$ is the same as $\displaystyle 3x^2= 3$ and, dividing both sides by 3, $\displaystyle x^2= 1$, 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". - Nov 27th 2009, 08:45 PMStroodle