Question

Form a quadratic polynomial whose one zero is the reciprocal of the other.​

Answer 1

Answer:

ax² - (a²+ 1)x + a = 0

Step-by-step explanation:

Let the roots be a and 1/a

Now sum of roots will be a + 1/a = (a² + 1)/a

and Product of roots will be (a) × 1/a = 1

Now we know that

Quadratic Equation = x² - (sum of roots)x + (product of roots)

= x² - [(a²+1)/a]x + 1 = 0

Multiplying both sides by a we get

ax² - (a²+ 1)x + a = 0