Question

p(y)= 5y^2-7y+1 find α&β​

Answer 1

Right Question: p(y)= 5y²-7y+1 find $\frac{1}{ \alpha }$ and $\frac{1}{ \beta }$

Since $\alpha \: and \: \beta$ are the zeroes of the polynomial 5y² - 7y + 1

Sum of the roots = α+β = $\frac{ - b}{a}$ $= - \frac{( - 7)}{5}$ $= \frac{7}{5}$

Product of the roots = αβ = $\frac{c}{a}$ $= \frac{1}{5}$

Now,

$\frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha + \beta }{ \alpha. \beta }$

$= \frac{7}{5} \div \frac{7}{5}$

= 7