Question

find quadratic equation whose roots are reciporcal of roots of equation 3x^2-5x-2

Answer 1

Check the attachment.

Answer 2

Heya user !!

Here's the answer you are looking for

Let the roots of the equation, 3x² - 5x - 2 be P and q.

So,
☛ sum of roots

= p + q

= -b/a

= -( -5 )/3

= 5/3

☛product of roots

= pq

= c/a

= -2/3


⏩For the required equation, the roots are 1/p and 1/q.

So,
☛sum of roots

$= \frac{1}{p} + \frac{1}{q} \\ \\ = \frac{p + q}{pq} \\ \\ = \frac{ \frac{5}{3} }{ \frac{ - 2}{3} } \\ \\ = \frac{ - 5}{2}$



☛ Product of roots

$= \frac{1}{p} \times \frac{1}{q} \\ \\ = \frac{1}{pq} \\ \\ = \frac{1}{ \frac{ - 2}{3} } \\ \\ = \frac{ - 3}{2}$


➡️ If roots of an equation are a and b, the the equation can be represented as

x² - (a + b)x + (ab)⬅️

Therefore, the required equation is

$= {x}^{2} - ( \frac{1}{p} + \frac{1}{q} ) x+ ( \frac{1}{p} . \frac{1}{q} ) \\ \\ = {x}^{2} - ( \frac{ - 5}{2} )x + ( \frac{ - 3}{2} ) \\ \\ = {x}^{2} + \frac{5x}{2} - \frac{3}{2} \: \: \: \: (answer)$


★★ HOPE THAT HELPS ☺️ ★★