# roots

## 03 - Solved Problems Involving Exponents and Radicals

Solve for $x$ from the following equations:

- $\left( \dfrac{x^2 - 15}{x} \right)^2 - 16\left( \dfrac{15 - x^2}{x} \right) + 28 = 0$

- $\dfrac{x}{\sqrt{x} + \sqrt{9 - x}} + \dfrac{x}{\sqrt{x} - \sqrt{9 - x}} = \dfrac{24}{\sqrt{x}}$

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## 02 - Solution to Radical Equations

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

- $\sqrt{(4 - x^2)^3} + 3x^2\sqrt{4 - x^2} = 0$

- $\dfrac{1}{3x - 2} - \dfrac{8}{\sqrt{3x - 2}} = 9$

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## Example 03 - Sum and product of roots of quadratic equation

## Example 02 - Quadratic equation problem

**Problem**

Determine the equation whose roots are the reciprocals of the roots of the equation 3x^{2} - 13x - 10 = 0.

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## 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 *x*^{2}*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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