If p, q are the roots of the Quadratic equation ax2 + bx + c = 0. Then what is the equation whose roots are 1/p, 1/q ?

If p, q are the roots of the Quadratic equation ax2 + bx + c = 0. Then what is the equation whose roots are 1/p, 1/q ? Correct Answer cx² + bx + a = 0

Given

p, q are the roots of ax2 + bx + c = 0

Formulae Used

Sum of roots = -b/a

Product of roots = c/a 

a Quadratic Equation can be written as x² – ( sum of roots )x + ( product of roots ) = 0

Calculation

From ax2 + bx + c = 0, we get p + q = -b/a, pq = c/a

The Quadratic equation with roots 1/p, 1/q = x² – (1/p + 1/q)x + 1/pq = 0

1/p + 1/q = (p + q)/pq

⇒ (-b/a) / (c/a) = -b/c

1/pq = a/c

⇒ x² – (-b/c)x + a/c = 0

⇒ cx² + bx + a = 0

∴ The required equation is cx2 + bx + a = 0