To find the sum and product of the roots for the quadratic equation $5x^2 - 4x + 2 = 0$, we can use the following formulas derived from Vieta's relations:

1. Sum of the roots: $\text{Sum of the roots} = -\frac{b}{a}$ where $a$ is the coefficient of $x^2$, and $b$ is the coefficient of $x$.

2. Product of the roots: $\text{Product of the roots} = \frac{c}{a}$ where $a$ is the coefficient of $x^2$, and $c$ is the constant term.

For the given quadratic equation $5x^2 - 4x + 2 = 0$:

• $a = 5$
• $b = -4$
• $c = 2$

Sum of the roots:

$\text{Sum of the roots} = -\frac{-4}{5} = \frac{4}{5}$

Product of the roots:

$\text{Product of the roots} = \frac{2}{5}$

So, the sum of the roots is $\frac{4}{5}$ and the product of the roots is $\frac{2}{5}$.

Would you like further details or explanations?

Here are 5 related questions to expand your understanding:

1. How do Vieta's formulas apply to cubic equations?
2. Can you find the discriminant of this quadratic equation?
3. How are the roots related to the graph of the quadratic function?
4. How can you find the actual roots of this quadratic equation using the quadratic formula?
5. What does the sum of the roots tell us about the symmetry of the parabola?

Tip: For any quadratic equation $ax^2 + bx + c = 0$, Vieta's relations offer quick insights into the relationships between the coefficients and the roots without solving the equation explicitly.