roots

03 - Solved Problems Involving Exponents and Radicals

Solve for $x$ from the following equations:

  1. $\left( \dfrac{x^2 - 15}{x} \right)^2 - 16\left( \dfrac{15 - x^2}{x} \right) + 28 = 0$
     
  2. $\dfrac{x}{\sqrt{x} + \sqrt{9 - x}} + \dfrac{x}{\sqrt{x} - \sqrt{9 - x}} = \dfrac{24}{\sqrt{x}}$

02 - Solution to Radical Equations

Determine the value of $x$ from the following equations:

  1. $\sqrt{(4 - x^2)^3} + 3x^2\sqrt{4 - x^2} = 0$
     
  2. $\dfrac{1}{3x - 2} - \dfrac{8}{\sqrt{3x - 2}} = 9$
     

Example 03 - Sum and product of roots of quadratic equation

Problem
Find the sum and product of roots of the quadratic equation x2 - 2x + 5 = 0.
 

Example 02 - Quadratic equation problem

Problem
Determine the equation whose roots are the reciprocals of the roots of the equation 3x2 - 13x - 10 = 0.
 

Quadratic Equations in One Variable

Quadratic Equation
Quadratic equation is in the form
 

$ax^2 + bx + c = 0$

Where
a, b, & c = real-number constants
a & b = numerical coefficient or simply coefficients
a = coefficient of x2
b = coefficient of x
c = constant term or simply constant
a cannot be equal to zero while either b or c can be zero
 

 
 
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