finding zeros?

Question

with out a calculator how could i find the zeros of the following polynomial: x^2 -2x +4

i know that it is an imaginary answer but i dont know how to find it.

Answer 1

x^2 -2x +4 = 0
(x^2 -2x +1)+3 = 0
(x-1)^2 = -3
x = 1 +/- sqrt(-3)

Answer 2

To find the zeros of a polynomial P(x) you need to solve

P(x) = 0

The polynomial you listed is called a quadratic, with a generalized form

ax^2 + bx + c = 0

where a, b, and c are constants. For quadratic polynomials a formula exists for the zeros:

x = (-b +/- sqrt(b^2-4ac))/2a)

In this case a = 1, b = -2, and c = 4

substituting into the formula you can find the roots. Since b^2-4ac is less than zero, the answer is a complex number

Answer 3

cw's method is called "completing the square."
Abe_Taha and flori used the Quadratic Equation.

Both methods are good to know. If you write programs like me, you may prefer the Quadratic Equation method.

Answer 4

For finding zeros of polynomial x^2 - 2x +4 use following formula and standard polynomial ax^2 +bx+c
zeros are x= -b + - square root of b^2-4ac
..............................................
2a
on comparing given equation with standard equation .a=1, b= -2
c= 4

so x = - (-2) + - square root of (-2)^2 - 4 *1*4
....................................................................
2*1
x = 2 + - square root of 4 -16
............................................
2
x = 2 + - square root of -12
.......................................
2
x =2+-3.46i
................
2
x= 1+-1.73 i
so zeros are 1+1.73 i and 1-1.73 i

Answer 5

Quadratic equation tells me its...

(+-)i(sq.3)