How quadratic formula comes?
Consider the quadratic equation \(ax^2 + bx + c = 0\), where \(a \ne 0\).
Let us find the roots of this equation by the method of completing the square.
Divide the equation by \(a\).
Move the constant to the right side.
Add the square of one half of coefficient of \(x\) on both sides.
Taking square root on both sides.
Therefore, the roots of \(ax^2 + bx + c = 0\) are and .
The formula for finding the roots of the quadratic equation \(ax^2 + bx + c = 0\) is:
This formula is known as the quadratic formula.
1. Find the roots of \(2x^2 + 3x - 77 = 0\) by using quadratic formula.
The given equation is \(2x^2 + 3x - 77 = 0\).
Here, \(a = 2\), \(b = 3\) and \(c = -77\).
Substitute the given values in the formula.
\(x =\) or \(x = -7\)
Therefore, the roots of the given equation are \(-7\) and .