Question

The roots of the quadratic equation ax2 + bx + c = 0 will be reciprocal to each other if

Answer 1

 ans :  a = c,
 
Let α be the first root .
Then the other root is 1/α

∵product of roots = c/a ... ( from the given equation )
∴α*1/α = c/a 
∴1 = c/a
i.e a=c

Answer 2

Answer:

Step-by-step explanation:

The roots of ax2+bx+c=0 are

−b±b2−4ac−−−−−−√2a

Given that the roots are reciprocal to each other.

⇒−b+b2−4ac−−−−−−√2a=2a−b−b2−4ac−−−−−−√

⇒4a2=b2−b2+4ac

⇒a−c=0