Question

Sum of roots is -1 and sum of their reciprocal is 1/6
then equation is
(a) x2 - 6x + 1 = 0
(b) x² – x+6=0
(c) 6x²+x+1=0
(d) x2 + x - 6 = 0
​

Answer 1

Answer

x² + x - 6 = 0

Solution

As given that :-

Sum of roots = -1

Sum of reciprocal of their roots = 1/6

Let the roots of equations as $\alpha$ and $\beta$

As we know that :-

$\alpha + \beta = - 1 = \frac{ - b}{a}$

Now we got value of -b/a and :-

$\frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{1}{6}$

$\frac{ \alpha + \beta }{ \alpha \beta } = \frac{1}{6}$

As we have already given the value of

$\alpha + \beta$

$\frac{ - 1}{ \alpha \beta } = \frac{1}{6}$

$\alpha \beta = - 6 = \frac{c}{a}$

We got value of of c/a . Now let a = k

→b = k

→c = -6 k

Now equation will be :-

kx² + kx -6k

k ( x² + x - 6 )

Equation = x² + x - 6 .