Question

factorise the polynomial
x^2-2x+5​

Answer 1

Step-by-step explanation:

x^2-2x+5

by squaring the root

x^2-2(1)x+(1)^2-(1)^2=-5

it's a identity a2+2ab+b2=(a+b)^2

that's why,

(x-1)^2=-5+(1)^2

(x-1)^2=-5+1

(x-1)^2=-4

x-1=√-4

we know that the value of under root (-4)is not defined.so, its roots are not possible

Answer 2

Answer:

The given polynomial can't be factorized.

Step-by-step explanation:

x² - 2x + 5 = 0

Here, a = 1, b = -2, c = 5

So, D = b² - 4ac

= (-2)² - 4(1)(5)

= 4 - 20

= - 24

We know that when

• D ≥ 0, then the quadratic equation has real roots and
• when D < 0, then the quadratic equation has imaginary roots or we can say that its roots don't exist.

So, the given polynomial can't be factorized.