Question

Find the nature of the quadratic equation x^2-2x+4

Answer 1

Answer:

Hence the nature of quadratic equation is imaginary.

Step-by-step explanation:

$compare \: {x}^{2} - 2x + 4 \: \\ with \: a {x}^{2} + bx + c \\ a = 1 \: \: \: \: b = - 2 \: \: \: \: c = 4 \\ according \: to \: shree \: dharacharya \\ x = \frac{ - (b) \binom{ + }{ - } \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - ( - 2) \binom{ + }{ - } \sqrt{ {( - 2)}^{2} - 4 \times 1 \times 4 } }{2 \times 1} \\ = \frac{2 \binom{ + }{ - } \sqrt{4 - 16} }{2} \\ = \frac{2(2 \binom{ + }{ - } \sqrt{1 - 4}) }{2}$

$= 2 \binom{ + }{ - } \sqrt{3} i$