Question

if a and b are the roots of the quadratic equation 2x^2- 3x-6. find the equation whose roots are 1/a and 1/b​

Answer 1

GIVEN:

• $a \: and \: b \: is \: the \: roots\: of \: 2 {x}^{2} - 3x - 6 = 0 \: quadratic \: eqn$

TO FIND:

• $\: quadratic \: eqn \: \: having \: roots \: \frac{1}{a} and \: \frac{1}{b}$

SOLUTION:

• FOR ANY QUADRATIC EQUATION ${x}^{2} - sum \: of \: roots \: \times x + product \: of \: roots = 0$
• $from \: our \: given \: eqn \\ 2 {x}^{2} - 3x - 6 = 0 \\ devide \: both \: side \: with \: 2 \\ {x }^{2} - \frac{3}{2} x - \frac{6}{2} = 0 \\ \\ hance \\ (a + b) = \frac{3}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: a \times b = - \frac{6}{2} \\ hance \: \frac{a + b}{ab} = \frac{ \frac{3}{2} }{ - \frac{6}{2} } \: \: \: \: \: \: \: \: and \: \frac{1}{ab} = - \frac{1}{3} \\ \frac{1}{a} + \frac{1}{b} = - \frac{1}{2 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

HANCE THE QUADRATIC EQUATION WILL BE

• ${x}^{2} - ( - \frac{1}{2} )x - 3 = 0$

HOPE THIS IS HELPFUL...