1. Jan 1, 2005

### yawie

Hi
Does anyone know any good sites that offer Grade ten math exercises? It's for my sister. Canadian grade ten math, she's doing stuff like quadratic equations, factoring, linear equations.
Also can someone explain to me why when you factor an equation with the quadratic equation the answers signs are reversed from when you do it manually? Like when I do it manually I'll get x= -5, 4 but when I do it with the quadratic equation it becomes x= 5, -4
Thanks! I don't know how to explain it to my sis!

Yawie

Last edited by a moderator: Dec 9, 2008
2. Jan 1, 2005

### TenaliRaman

Yawie,

i really dont understand whats the problem. Can u clarify with an example?

-- AI

Last edited by a moderator: May 1, 2017
3. Jan 2, 2005

### yawie

Thanks! I'll go check that out!

for instance:
lets say for x^2 + 5x + 4
if i do it by trial and error the answer would be (x+4)(x+1)
however, if i do it with the quadratic formula...the complicated one. I don't know how to write it... the answer would be (x-4)(x-1) which doesn't work when u multiply them out.
btw how do u write out those complicated equations?

Thanks alot!
Yawie

Last edited by a moderator: Dec 9, 2008
4. Jan 2, 2005

### misogynisticfeminist

edit: oops sorry, misread the question.

5. Dec 9, 2008

its because the formula for factored form is y=a(x-s)(x-t), so since its -s and -t, you need to change the sign in front of each x value (or zero) before you put it in the equation manually.
for example if the quadratic equation gave you the roots x=5 and x=-3, you would need to switch them to -5 and 3 before putting them in the equation like so :
y=a(x-5)(x+3)
hope it helped! :D

6. Dec 9, 2008

### danago

By using the quadratic formula, you are essentially solving the following equation:

x^2 + 5x + 4 = 0

Which, as you obtained, has the two solutions x=-4 and x=-1.

Now when a quadratic equation is in the form:

(x-a)(x-b) = 0,

We know that EITHER x-a=0 or x-b=0 (or maybe both), since the product of two numbers can only be zero if one or both numbers are zero. Solving these two equations yields the solutions x=a and x=b. Can you now see why the sign reverses?

So in the example you gave, solving for its zeros gives the two solutions x=-4 or x=-1, therefore any factored form should have the same two zeros. If you use the one without changing the signs:

(x-4)(x-1),

and try plugging either x=-1 or x=-4 into it, you will see that it doesnt equal zero, so it cannot be the same quadratic.