Question

Quadratic Formula to solve the equation x^2- 4x = - 7

Answer 1

roots of the equation x^2- 4x = - 7 are  2+3i and 2-3i

What are the natures of root of quadratic equation?

Case I: $4ac > b^2$

The roots of the quadratic equation $ax^2 + bx + c = 0$are real and unequal when a, b, and c are real numbers, a 0, and the discriminant is positive.

Situation II:  $b^2$$-4ac$ =0

The roots and of the quadratic equation$ax^2 + bx + c = 0$  are real and equal when a, b, and c are real numbers, a 0, and the discriminant is zero.

Case III: $b^2$$-4ac$<0

The quadratic equation $ax^2 + bx + c = 0$ has roots when a, b, and c are real numbers, a 0, and the discriminant is negative, but these roots are not equal and are not real. We refer to the roots in this instance as fictitious.

Case IV: Perfect square and $b^2 - 4ac > 0$

The roots of the quadratic equation $ax^2 + bx + c = 0$  are real, rational, and unequal when a, b, and c are real numbers, a 0, and the discriminant is positive and perfect square.

Quadratic Formula $x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}$

$x^2- 4x = - 7$

$x^2-4x+7=0$

Here a = 1 , b = -4 , c = 7

using quadratic formula

$x={\frac {-(-4)\pm {\sqrt {(-4)^{2}-4(1)(7)}}}{2(1)}}$

$x={\frac {4\pm {\sqrt {-12}}}{2}}$

$x={\ {2\pm {\ 3i}}$

Learn more about quadratic equation from the link below

brainly.com/question/2279540

#SPJ1