Question

Find the quadratic equation whose roots are reciprocal of the equation 3x^2-20x+17=0

Answer 1

Here in the equation
$3 {x}^{2} - 20x + 17 \\ 3 {x}^{2} - 3x - 17x + 17 \\ 3x(x - 1) - 17(x - 1) \\ (3x - 17)(x - 1)$
So the zeroes of this equation are
$x \: = 17 \div 3 \\ x = 1$
We know that for making zeroes had to be reciprocal of these hence they are
$x = 3 \div 17 \: and \: \: x = 1$

We know that the equation is formed by
${x}^{2} - (sum \: of \: the \: zeroes)x \: + (product \: of \: the \: zeroes \: )$
${x}^{2} - (3 \div 17 + 1)x + 3 \div 17 \times 1$
${x}^{2} -( 20 \div 17)x + 3 \div 17$