Answer:
1. α²+β² = 25/36
2. 1/α+1/β = 1/2
Step-by-step explanation:
Formula :
Consider the quadratic equation ax² + bx + c = 0
Where x₁ and x₂ are the zeros of the equation.
Then
[tex]x_{1}+x_{2}=-\frac{b}{a} \\x_{1}\times x_{2}=\frac{c}{a}[/tex]
……………………………………
α and β are the zeros of the quadratic polynomial f(x) = 6x²+x-2
Then
[tex]\alpha +\beta =-\frac{1}{6}[/tex]
[tex]\alpha \times \beta =-\frac{1}{3}[/tex]
……………………
[tex]\alpha^{2} +\beta^{2} =\left( \alpha +\beta \right)^{2} -2\alpha \beta[/tex]
[tex]=\alpha^{2} +\beta^{2} =\left( -\frac{1}{6} \right)^{2} -2\times(-\frac{1}{3} )[/tex]
[tex]=\frac{25}{36}[/tex]
………………………………
[tex]\frac{1}{\alpha } +\frac{1}{\beta } =\frac{\alpha +\beta }{\alpha \beta }[/tex]
[tex]=\frac{-\frac{1}{6} }{-\frac{1}{3} } =\frac{1}{2}[/tex]
