Thread: quadratic 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

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 ...

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

then the roots are $\displaystyle x = \pm 1$

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 $\displaystyle x = \sqrt{1} = 1 \textrm{ or } -1$

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 ....

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".

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 $\displaystyle 3x^2- 3= 0$, 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".

I was wondering about that. Thanks for the info