Introduction of quadratic equation

In this section, we will discuss about introduction of quadratic equation.
If a f(x) is a polynomial, then f(x)= 0 is called a polynomial equation. If f(x) is a quadratic polynomial then f(x) = 0 is a quadratic equation but only if the degree of that polynomial is 2. The standard form of quadratic equation is
$ax^{2}$ + bx + c = 0 , a $\neq$ = 0
where 'x' is a variable and a, b, c are called coefficients real or imaginary.

Examples on introduction of quadratic equation

1) 4$x^{2}$ -2x + 8 = 0 is a quadratic equation as the degree of this polynomial is 2.
a = 4
b = -2
c = 8

2) $x^{2}$ + 6x -10 = 0 is a quadratic equation as the degree of this polynomial is 2.
a = 1
b = 6
c = -10

3) $\frac{2}{3}x^{2}$ + x + 12 = 0 is a quadratic equation as the degree of this polynomial is 2.
a = $\frac{2}{3}$
b = 1
c = 12

4) $x^{2} -\frac{1}{3}$x -7 = 0 is a quadratic equation as the degree of this polynomial is 2.
a = 1
b = $-\frac{1}{3}$
c = -7

5) $2x^{2}$ - 11 = 0 is a quadratic equation as the degree of this polynomial is 2.
a = 2
b = 0
c = -11

6) -3x + 5 = 0 is not a quadratic equation as the degree of this polynomial is 1.

7) $15x^{2}$ -0.8x + 4 = 0 is a quadratic equation as the degree of this polynomial is 2.
a = 15
b = -0.8
c = 4

8) $0.1x^{2}$ + 0.18x + 12 = 0 is a quadratic equation as the degree of this polynomial is 2.
a = 0.1
b = 0.18
c = 12

9) $\frac{-4}{7}x^{2} + \frac{3}{4}x + \frac{2}{3}$ = 0 is a quadratic equation as the degree of this polynomial is 2.
a = $\frac{-4}{7}$
b = $\frac{3}{4}$
c = $\frac{2}{3}$

10) $\frac{11}{2}x^{2} - \frac{1}{6}x -\frac{1}{9}$ = 0 is a quadratic equation as the degree of this polynomial is 2.
a = $\frac{11}{2}$
b = $\frac{-1}{6}$
c = $\frac{-1}{9}$

11) 4$x^{3}$ + 9x + 1 = 0 is not a quadratic equation as the degree of this polynomial is 3.

12) 4$x^{3}$ -10 = 0 is not a quadratic equation as the degree of this polynomial is 3.

13) $x^{2}$ -16 = 0 is a quadratic equation as the degree of this polynomial is 2.
a = 1
b = 0
c = -16

14) $x^{2}$ -x + 1 = 0 is a quadratic equation as the degree of this polynomial is 2.
a = 1
b = -1
c = 1

15) $\frac{1}{x^{2}}$ -2x + 8 = 0 is not a quadratic equation as the degree of this polynomial is -2.


11th grade math

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