# What is Quadratic equation: Definition and 252 Discussions

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation that can be rearranged in standard form as

a

x

2

+
b
x
+
c
=
0

{\displaystyle ax^{2}+bx+c=0}
where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no

a

x

2

{\displaystyle ax^{2}}
term. The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions. If there is no real solution, there are two complex solutions. If there is only one solution, one says that it is a double root. A quadratic equation always has two roots, if complex roots are included and a double root is counted for two. A quadratic equation can be factored into an equivalent equation

a

x

2

+
b
x
+
c
=
a
(
x

r
)
(
x

s
)
=
0

{\displaystyle ax^{2}+bx+c=a(x-r)(x-s)=0}
where r and s are the solutions for x. Completing the square on a quadratic equation in standard form results in the quadratic formula, which expresses the solutions in terms of a, b, and c. Solutions to problems that can be expressed in terms of quadratic equations were known as early as 2000 BC.
Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation contains only powers of x that are non-negative integers, and therefore it is a polynomial equation. In particular, it is a second-degree polynomial equation, since the greatest power is two.

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3. ### I Find the roots of the quadratic equation by differentiation

The Solution of the Quadratic Equation By Differentiation Method
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9. ### Find the value of ##r## and ##s## in the given quadratic equation

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10. ### Solve the quadratic equation involving sum and product

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31. ### Quadratic equation to find max and min

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34. ### I Quadratic equation of two variables

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1. Determine the equation that represents the relationship between the power and the current when the electric potential difference is 24v and the resistance is 1.5 Ω. 2. Draw a graph of the parabola that corresponds to the equation found in (a). 3. Determine the current needed in order for...

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38. ### Discriminant and quadratic problem

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39. ### When to use quadratic equations?

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43. A

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44. L

### B Quadratic Equation with three variables

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45. S

### How to solve this quadratic equation?

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46. S

### B How do I solve this Quadratic Equation?

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47. T

### Quadratic equation for maximum compression of a spring

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