Question

If 𝜶 and 𝜷 are the zeroes of the polynomial $6y^2-7y+2$, find a quadratic polynomial whose zeroes are $\frac{1}{\alpha }$ , $\frac{1}{\beta }$.

Answer 1

Let us find the coefficients.
a = 6,
b = -7
c = -2

Step 1:
Find the sum and product of zeroes of the given polynomial


where 𝜶 and 𝜷 are the zeroes of the given polynomial.


Step 2:
Find the sum and product of zeroes of the required polynomial

Step 3: Find the required polynomial