Question

Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the
polynomial f(x) = ax2 +bx+c, a ≠0,c≠0.​

Answer 1

Answer:

$let \: \alpha \: \: \: \beta \: are \: the \: zeros \\ \alpha + \beta = \frac{ - b}{a} \\ \alpha \beta = \frac{c}{a} \\ \\ \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ - b}{c} \\ \frac{1}{ \alpha \beta } = \frac{a}{c} \: \\ required \: equation \: is \: k ({x}^{2} - ( \frac{ - b}{c})x + ( \frac{a}{c} ) )\\ = k( {x}^{2} + \frac{b}{c}x + \frac{a}{c} ) \\ let \: k = c \\ =c ( {x}^{2} + \frac{b}{c} x + \frac{a}{c} ) \\ = c {x}^{2} + bx + a \: is \: the \: required \: polynomial$