Question

find all zeroes of f(x) =x^2-2x+1

Answer 1

$\green{\bold{\underline{ ☆ UPSC-ASPIRANT ☆} }}$

$\red{\bold{\underline{\underline{QUESTION:-}}}}$

find all zeroes of f(x) =x^2-2x+1

$\huge\bigstar\huge\tt\underline\red{ᴀɴsᴡᴇʀ }\bigstar$

$➫ {x}^{2} - 2x + 1 = 0$

$➫ {x}^{2} - x - x + 1 = 0$

$➫x(x - 1) - 1(x - 1)$

$➫(x - 1)(x - 1)$

$➫x = 1$

➫ The zeroes are( 1,1)

HOPE IT HELPS YOU..

_____________________

Thankyou:)

Answer 2

$\huge\underline{★Answer:-}$

Given :-

The polynomial is x² -2x + 1

To find:-

The zeroes of the polynomial

Solution:-

⇒ f ( x ) = x² -2x + 1

⇒f(x) = 0

⇒x² -2x +1 = 0

Now , by doing Middle term Factorisation,

⇒x² - ( 1 + 1 ) x + 1 = 0

⇒x² - x -x + 1 = 0

⇒x ( x - 1 ) - 1 ( x - 1 ) = 0

⇒( x - 1 ) ( x - 1 ) = 0

Either ...

⇒( x - 1) = 0

⇒x = 1

or ...

⇒( x - 1) = 0

⇒x = 1

Therefore, The zeroes are 1 , 1

As , it has two zeroes that means it is a quadratic polynomial.

Also the degree of the polynomial is 2

Now,

Things To Know:-

• The standard form of a quadratic polynomial is ax² + bx + c = 0 ( where a ≠ 0 ) and ( a and b are real numbers )

• A polynomial having highest power of "x" variable will be the degree of it .

• The degree of a polynomial alaways represent the number of zeroes of the polynomial .

Here are some of the examples of quadratic polynomial -

• x² + 3x -10 =0

• x² + 7x + 12 = 0

• x² -2x -8 =0

• 2x² -x -6 =0

• 5x² -4 -8x = 0

you can find out the zeroes of it in the same way as i have done in the above solution .