Question

The equation whose roots are reciprocal of the roots of the equation 3{{x}^{2}}-20x+17=0
is [DCE 2002]
A) 3{{x}^{2}}+20x-17=0 B) 17{{x}^{2}}-20x+3=0 C) 17{{x}^{2}}+20x+3=0 D) None of these

Answer 1

Hi ,.

given quadratic

equation 3x² - 20x + 17 = 0

3x² - 3x - 17x + 17 = 0

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

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

x - 1 = 0 or 3x - 17 = 0

x = 1 or x = 17/3

Therefore

1 , 17/3 are two roots of the given quadratic

equation ,

The reciprocals of above roots are

1 , 3/17

sum of the roots = 1 + 3/17

= ( 17 + 3 )/17

= 20/17 ---( 1 )

product of the roots = ( 1 ) × ( 3/17 )


= 3/17 ---( 2 )

Now ,

required quadratic equation is

x² - ( sumof the roots )x + product of the roots = 0

x² - ( 20/17 ) x + 3/17 = 0

17x² - 20x + 3 = 0

Therefore ,

Option ( B ) is correct.

I hope this helps you.

: )