Quadratic Formula
ax2+bx+c=0 ……. x = -b ± √(b² – 4ac)/2a
The quadratic formula is a formula that is used to solve quadratic equations. A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and x is the variable. The quadratic formula is:
x = (-b ± sqrt(b^2 – 4ac)) / 2a
This formula provides the values of x, which are the solutions to the quadratic equation. The formula can be used for all quadratic equations, regardless of the values of a, b, and c.
To use the quadratic formula, you need to plug in the values of a, b, and c into the formula, and then simplify the expression to find the value(s) of x. If the expression under the square root sign is negative, then the equation has no real solutions.
For example, let’s solve the quadratic equation x^2 + 4x + 3 = 0 using the quadratic formula:
a = 1, b = 4, c = 3
x = (-4 ± sqrt(4^2 – 4(1)(3))) / 2(1)
x = (-4 ± sqrt(16 – 12)) / 2
x = (-4 ± sqrt(4)) / 2
x = (-4 ± 2) / 2
The two solutions of the quadratic equation are:
x = -1 and x = -3
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