y1 + y2 = 0
y1*y2 = -19
Explanation:
The equation: y^2 - 19 = 0
Using Vieta's formula for equation in the form:
ax^2 + bx + c = 0
sum of roots = -b/a
Product of roots = c/a
Comparing the equation above with the equation in the question:
y^2 + 0x -19 = 0
coefficent of y^2 = a = 1
coefficient of x = b = 0
The constant = c = -19
[tex]\begin{gathered} sumofroots=y_1+y_2 \\ \text{sum of roots = }\frac{-0}{1}\text{ = 0} \\ sum\text{ of roots = }0 \end{gathered}[/tex]
[tex]\begin{gathered} Productofroots=y_1\times y_{2\text{ }}\text{= }\frac{c}{a} \\ \text{Product of roots = }\frac{-19}{1} \\ \text{product of root = -19} \end{gathered}[/tex]
Hence:
[tex]\begin{gathered} y_1+y_2=\text{ 0} \\ y_1\times y_2\text{ = -19} \end{gathered}[/tex]
