ex.:x squared-5x +4.to find x we factor out..(x-4)(x-1). now here's d question,y do we have to equate it to 0?

Answer 1

Yes, you have to equate it to zero.

When you factor a quadratic, you have the product of two terms. When the product of two terms equals zero, either the first term equals zero, or the second term equals zero.

When the product of two terms equals something other than zero such as ten, it is not true that either the first term equals ten or the second term equals ten.

Answer 2

No - you have factored it out so that x^2-5x+4 = (x-4)(x-1). You only have to set it to zero if you want to know for what values of x does the equation equal zero (4,1).

The equation means that if you take a number e.g. 54 that can be represented in the form x^2-5x+4 (in this case 10^2 - 5*10 + 4) then it can be factored into (x-4) and (x-1) e.g. in this case (10-4)(10-1) i.e. 9 * 6

Answer 3

If given in the form of an equation:-
x² - 5x + 4 = 0
(x - 4).(x - 1) = 0
x = 4 , x = 1

It may be that you are unsure of what happens after
(x - 4).(x - 1) = 0

x - 4 is a number A,say
x - 1 is a number B,say
A X B = 0 and therefore:-
A = 0 or B = 0
(x - 4) = 0 or (x - 1) = 0
x = 4 , x = 1

Hope this helps.

Answer 4

In this case, I don't think you have to, unless you need to find the zeroes. If you just want to factor it, you don't need it to equate to 0.

x^2-5x+4
---*--- = 4 and ---+--- = -5
-1*-4 = 4 and -1 + -4 = -5
x^2 -x -4x +4
x(x-1) -4(x-1)
(x-4)(x-1)

But if you have to find the zeroes after, then you need to equate it to 0 so you can isolate x :
0 = (x-4)(x-1)
0 = x-4
4 = x
0 = x-1
1 = x

Answer 5

actually, it's more the other way around. you should have started with an equation like
x squared-5x +4 = 0.

then to solve such an equation, you factor the polynomial. if it weren't equal to zero (for example if it were equal to 6 instead), factoring wouldn't help you solve it; you'd have to move the 6 to the left side first so that it's equal to zero.

the point is that the technique of factoring is specifically used to find when a polynomial is equal to zero.

Answer 6

yes so you can find the roots:

x-4=0 >>> x=4
x-1 = 0 >>> x=1
so 4 and 1 are the roots of this equation.