Question

if alpha and beta are zeroes of the polymomial 3x^2 -4x -7 , then form a quadratic polynomial whose zeroes are 1/ alpha and 1/beta​

Answer 1

Step-by-step explanation:

$\huge \purple{ \mathcal{ {he}^{llo} \: {cu}^{rious} \: {it}^{s} \: {bad}^{itya} }}$

$given \: that \\ \alpha \: and \: \beta \: are \: zeroes \: of \:given \: eqution$

we know that sum of zeroes = -(coeff of x)/(coeff of x²)

and product of zeroes = (constant term)/(coeff of x²)

$so \\ \alpha + \beta = \frac{ - ( - 4)}{3} = \frac{4}{3} \\ and \\ \alpha \beta = \frac{ - 7}{3}$

$so \: \\ \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha + \beta }{ \alpha \beta } \\ = > \frac{ - 4}{7} \\ and \\ \frac{1}{ \alpha } \times \frac{1}{ \beta } = \frac{1}{ \alpha \beta } \\ = > \frac{ - 3}{7}$

so the polynomial having zeroes

$\huge \frac{1}{ \alpha } \: and \: \frac{1}{ \beta } \: is$

x²-(-4/7)x+(-3/7)

or

,

7x²+4x-3

hope it helps