Question

find the quadratic equation whose roots are reciprocals of the roots of the equation 3x2-20x+17=0

Answer 1

hope it will help you

Answer 2

3x² - 2x + 17 = 0

3x² - 17x -3x +17 = 0

x (3x -17 ) -1 ( 3x-17 ) = 0

( x - 1 ) ( 3x - 17 ) = 0

=> ( x-1 ) = 0

x = 1

=> ( 3x - 17 ) = 0

x = 17/3

as given in question that roots of new equation is reciprocal of old one

then

roots of new equation will be

x = 1

x = 3/17

=> To form quadratic equation we have to find sum and product of roots

So,

☣Sum of roots = 1 + 3/17

= (17 + 3) /17

= 20/17

☣ Product of roots = 1× 3/17

= 3/17

=> To find quadratic equation we have formula as

${x}^{2} - (sum \: of \: roots \: )x + (product \: of \: roots)$

So, putting those value in formula

x² - ( 20/17)x + 3/17

17x² -20x +3

So, new quadratic equation is
17x² -20x +3