First slide

Theory of equations

Question

The equation whose roots are reciprocal of the roots of the equation
$3 x^{2} - 20 x + 17 = 0$ is

Moderate

A

$3 x^{2} + 20 x - 17 = 0$
B

$17 x^{2} - 20 x + 3 = 0$
C

$17 x^{2} + 20 x + 3 = 0$
D

None of these

Solution

Given equation $3 x^{2} - 20 x + 17 = 0$
$\Rightarrow (x - 1) (3 x - 17) = 0 \Rightarrow x = 1, \frac{17}{3}$
Reciprocal roots are 1 and $\frac{3}{17}$
$∴$ Equation is $x^{2} - (1 + \frac{3}{17}) x + \frac{3}{17} = 0$
$\Rightarrow 17 x^{2} - 20 x + 3 = 0$

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