Let's first rewrite the given equation $5x^2 - 8 = 22x$ in standard form:

$5x^2 - 22x - 8 = 0$

For a quadratic equation of the form $ax^2 + bx + c = 0$:

• The sum of the roots is given by $-\frac{b}{a}$.
• The product of the roots is given by $\frac{c}{a}$.

For the equation $5x^2 - 22x - 8 = 0$:

• $a = 5$
• $b = -22$
• $c = -8$

Sum of the roots:

$\text{Sum} = -\frac{b}{a} = -\frac{-22}{5} = \frac{22}{5}$

Product of the roots:

$\text{Product} = \frac{c}{a} = \frac{-8}{5} = -\frac{8}{5}$

Final Answer:

• The sum of the roots is $\frac{22}{5}$.
• The product of the roots is $-\frac{8}{5}$.

Would you like more details on how to solve this or any related topic?

Here are five related questions you might find interesting:

1. How do you find the exact roots of the equation $5x^2 - 22x - 8 = 0$?
2. What is the significance of the sum and product of roots in solving quadratic equations?
3. Can you solve quadratic equations using the factoring method, and how would it apply to this equation?
4. What are the implications if the sum or product of roots turns out to be zero?
5. How can the sum and product of roots be used to reconstruct the original quadratic equation?

Tip: The discriminant of a quadratic equation can help you determine the nature of the roots (real and distinct, real and equal, or complex) before solving the equation.