Find the quadratic equation whose roots are reciprocal of

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

1. 17x² - 20x + 3 = 0
2. 17x² + 20x + 3 = 0
3. 17x² - 20x - 3 = 0
4. None of these

Correct Option: A

The given quadratic equation is
3x² - 20x +17 = 0 .......(1)
Compare with ax² + bx + c = 0, we get
a = 3, b = −20, c = 17
The roots of (1) are given by

x =	- b ± √b² - 4ac	=	20 ± √400 - 4(3)(17)
	2a		2 × 3

x =	20 ± √196	=	20 + 14	,	20 - 14
	6		6		6

x =	34	,	6	=	17	, 1
	6		6		3

Hence the roots of (1) are	17	and 1.
	3

So we have to form an equation whose are	3	and 1
	17

Sum of the roots =	3	+ 1 =	20
	17		17

Product of the roots =	3	x 1 =	3
	17		17

Hence, the required equation is

x² -	20	x +	3	= 0
	17		17

⇒ 17x² - 20x + 3 = 0.