Question

for the quadratic equation x^2-6x+5=0find(alpha)^-1+(beta)^-1 where alpha and beta are roots​

Answer 1

Answer:

6/5

Step-by-step explanation:

α and β are the roots of the equation.

Sum of roots = α + β = -b/a = 6/1 = 6

product of roots = αβ = c/a = 5/1 = 5

1/α + 1/β = α + β / αβ = 6/5

Answer 2

Solution:

$p(x)=x^{2} -6x+5\\ \\ \alpha +\beta =\frac{-b}{a}=\frac{-(-6)}{1} =6 \\ \\ \alpha \beta =\frac{c}{a} =\frac{5}{1} =5\\ \\ \alpha ^{-1} +\beta ^{-1} =\frac{1}{\alpha } +\frac{1}{\beta }\\  \\ =\frac{\alpha+\beta  }{\alpha \beta } \\\\=\frac{6}{5}$

Answer =  $\frac{6}{5}$