Question

If ,α,β,γ are the zeros of p(x)=5x^3+2x^2-3x+1 then find the value of 1/α+1/β+1/γ

Answer 1

Step-by-step explanation:

follow this example

I hope this may help you

Answer 2

Comparing the polynomial with ax³+bx²+cx+d= 0

we get

a=5, b=2, c=-3 and d=1

$\alpha + \beta + \gamma = \frac{ - b}{a} = \frac{ - 2}{5} \\ \alpha \beta + \beta \gamma + \gamma \alpha = \frac{c}{a} = \frac{ - 3}{5} \\ \alpha \beta \gamma = \frac{ - d}{a} = \frac{ - 1}{5} \\ now \\ \frac{1}{ \alpha } + \frac{1 }{ \beta } + \frac{1}{ \gamma } \\ = \frac{ \beta \gamma + \alpha \gamma + \alpha \beta }{ \alpha \beta \gamma } \\ = \frac{ \frac{ - 3}{5} }{ \frac{ - 1}{5} } \\ = \frac{ - 3}{5} \times \frac{5}{ - 1} \\ = 3$