What is a Quadratic Equation?
We employ a different type of mathematical equation to solve a variety of real-world problems one such equation that we often use is the quadratic equation. In simpler terms, a quadratic equation is defined as the equation with the highest order of 2. Quadratic equation is written as:
The easiest way to solve the quadratic equation is to factor the quadratic for the value of 'x.' We equate each factor equal to zero and then find the solution for each factor.
Where factoring seems challenging, the quadratic formula makes it easier to find the solutions.
If you use the general quadratic equation,
ax2 + bx + c = 0.
Then you will be able to find the roots of the quadratic equation, i.e., values of 'x' for which the equation is being solved
The quadratic formula also uses 'a' , 'b' , and 'c' to represent the numerical coefficients. Quadratic Formula is written as:
X = (-b ± √(b2 ) - 4ac / 2a.
Let's understand this better with an example: WORKED EXAMPLE ---
First, identify the values for a, b, and c. make sure you write your equation in the format of quadratic equation, i.e., ax2 + bx + c = 0
Let's assume if we have, x2 + 4x - 21 = 0.
a is the coefficient with x2, so in this case, we have a = 1.
b is the coefficient with x, here b = 4.
c is the numerical constant, so here c = -21.
replace all the values in the formula:
x = (-4 ± √16-4.1.(-21)) / (2.1)
solving the equation for the value of x.
x = (-4 ± √100) / 2.
x = (-4 ± 10)/2.
x = (-4+10)/2, (-4-10)/2.
x = 6/(2 ) ,(-14)/2.
x = 3, -7.
the values of 'x' are 3, and -7.