Vieta Theorem (Basic) - Math All Star

Vieta Theorem (Basic)

11 practice problems to polish students' basic Vieta theorem skills. Here are some examples included in this exercise:

Let $x_1$ and $x_2$ be the two roots of equation $x^2 âˆ’ 3x + 2 = 0$. Find the following values withoutcomputing $x_1$ and $x_2$ directly.

i) $x_1^4 + x_2^4$

ii) $x_1 - x_2$

(Note: for (i) above, how many different solutions can you find?)

Find the sum of all possible integer values of $a$ such that the equation $(a + 1)x^2-(a^2 + 1)x + (2a^2 âˆ’ 6) = 0$ is solvable in integers.

(2604) If real number $m$ and $n$ satisfy $mn\ne 1$ and $19m^2+99m+1=0$ and $19+99n+n^2=0$, what is the value of $\frac{mn+4m+1}{n}$?

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