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# A maths problem regarding zeroes of a polynomial?

i have a problem in maths

i m studying in class tenth

it was given in my NCERT book that

suppose we take

2x^2 - 8x + 6 = 2(x-1)(x-3)

then it was given that

x-1=0

x-3=0

so 1 and 3 are zeroes of the polynomials

my problem is that "how we can say that "x-3=0" and "x-1=0"

it was nowhere mentioned about dis???

plzz help urgently!

i have a problem in maths

i m studying in class tenth

it was given in my NCERT book that

suppose we take

2x^2 - 8x + 6 = 2(x-1)(x-3)

then it was given that

x-1=0

x-3=0

so 1 and 3 are zeroes of the polynomials

my problem is that "how we can say that "x-3=0" and "x-1=0"

it was nowhere mentioned about dis???

plzz help urgently!

hey i saw jake's answer n i think its best

i could understand a bit

but then until u explained was ok

after that

either of the numbers (x-1, x-3) must be zero

i agree to that but in my book its been explained

that a quadratic polynomial has two zeroes n when it is made into a graph it forms a parabola

so i wanted to ask that how can we both of them i.e. x-1, x-3 as zeroes?????

### 7 Answers

- Anonymous10 years agoFavorite Answer
well you should understand what zero of a polynomial means

it is what values of x will make the polynomial zero

now 2(x-1)(x-3) is your polynomial

zero of the polynomial means 2(x-1)(x-3) = 0 or (x-1)(x-3) = 0

this is the product of two numbers, lets ignore 2 for the time being

the product of two numbers x-1 and x-3 is zero

can you think of two numbers which multiply to get zero ?

the only way you can get zero by multiplication is when one of the numbers is zero

which means either x-3 = 0 ( implying x = 3) or x-1 = 0 ( implying x=1)

i hope this answers and clarifies your question

its pretty straightforward

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- Anonymous10 years ago
For this Particular problem zero's of the Polynomial means the Solution of 2x^2 - 8x + 6 = 0, or

2(x-1)(x-3)=0, or the value of x for which value of the expression becomes zero. thus if 2(x-1)(x-3)=0 then it means product of 2 , (x-1) & (x-3) zero. Since 2 cant be equl to 0, so either the value of x-1 or that of x-3 = 0. which implies that either x=1 or 3.

Thats it.

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- 10 years ago
Let's take a general polynomial y=(x-a)(x-b)(x-c)..............(x-n). Any zero will make it zero.

=>to find a zero we can write a polynomial equation (x-a)(x-b)(x-c)..............(x-n) = 0. Put x = a, then the factor (x-a) will be 0 as (a-a) is zero and no matter if you multiply any quantity it will be 0. Similarly b, c, ........n all make it = 0. Hence in maths we state that as a, b, c, d.......n, make this polynomial = 0 these are its zeroes.

In your case y = 2(x-1)(x-3).

It will be zero if x-1 =0 or x-3 = 0. It implies x = 1 and x = 3, both make it = 0.

So these are it's zeroes.

Since, equating each factor to 0 will give a zero of polynomial, we writ x-a=0 , x-b=0.....x-n = 0

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- 10 years ago
x-1=0 so what is x? x must be 1, since 1-1=0

Like wise, x-3=0, then x must be three.

They equate it to 0 so you can find the value of the x.

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- ranjankarLv 710 years ago
2x^2 - 8x + 6 = 0

So 2(x-1)(x-3) = 0

So either

x- 1 = 0 i.e x = 1

OR

x- 3 = 0 i.e x = 3

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- 10 years ago
we have the eqn f(x) = 2(x-1)(x-3);

Zeroes of the polynomials are points which it passes through the x-axis, to get these points, our f(x) should be zero. so in this eqn, x must be 1 or 3 for the eqn to be zero . . . :))

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- Anonymous10 years ago
u dont have any other methodd for it

either one has to be taken as zero otherwise there wud b no number by which if we put in place of x then it will nil the whole eqn

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