Question

how to find roots of a given equation

Answer 1

consider the equation is in form
ax²+bx+c=0
then the two roots are given by
$\frac{-b+ \sqrt{b^2-ac} }{2a}, \frac{-b- \sqrt{b^2-ac} }{2a}$

Answer 2

A quadratic equation is a second-order polynomial equation expressed in a single variable, x, with a ≠ 0: ax2+bx+c=0

Because the quadratic equation is a second-order polynomial equation, it must have two solutions. These solutions may both be real, or complex.

The root of a function, such as a parabola, is the x value where the output value y is 0.The roots can be found by completing the square:x2 + (b/a)x = -c/a(x + b/2a)2 = c/a + b2/4a2 = b2-4ac/4a2x + b/2a = ≠√b2-4ac/2aSolving

for x results in the quadratic formula,

Plug in for a, b, and c. These are taken from the equation ax2+bx+c=0
Remember that a square root can be both positive and negative.
 
Don't fall into the trap of only writing down one answer when there should be two.

You can also set the quadratic equal to zero (0) and factor or complete the square, but that's the same thing as using the formula if you recall from the proof.