Question

Write the Nature of roots of x2-2x+7 = 0.​

Answer 1

Given:

The given equation is, $x^{2} -2x+7=0$.

To find:

The nature of the roots of the given equation.

Explanation:

$x^{2} -2x+7=0$

Here,$a=1,b=-2,c=7$.

Discriminant, $D=b^{2}-4ac$

$D=(-2)^{2} -4(1)(7)$

$D=4-28$

$D=-24 < 0$

Therefore, the roots are unreal or imaginary.

Answer 2

In algebra, a quadratic equation is any equation that can be rearranged in standard form as $ax^{2}+bx+c=0$ where x represents an unknown, and a, b, and c represent known numbers, where $a \neq 0$. If $a = 0$, then the equation is linear, not quadratic, as there is no $ax^2$ term.

Given: The given equation is, $x^2-2+7=0$ .

Find: The nature of the roots of the given equation.

Explanation:

$x^2-2x+7=0$

Here, $a=1,b=-2,c=7$

Discriminant, $D=b^2-4ac$

$D=(-2)^2-4(1)(7)$

$D=4-28$

$D=-24 < 0$

Therefore, the roots are unreal or imaginary.