If a, ẞ are zeroes of the quadratic polynomial x² – 5x + 6, form another quadratic polynomial whose zeroes are 1 1 αβ

Question :If a, ẞ are zeroes of the quadratic polynomial x² – 5x + 6, form another quadratic polynomial whose zeroes are 1 1 αβ

The correct answer :The given quadratic polynomial is x² – 5x + 6.

We know that sum of zeroes (a and ß) = a + ß = 5 Product of zeroes (a and ß) = aß = 6

As 1 and 1/α are zeroes of the new polynomial, we can write it as: (x – 1)(x – 1/α) = 0

Multiplying both sides by α, we get: α(x – 1)(αx – 1) = 0

Expanding the above equation, we get: αx² – (α + 1)x + 1 = 0

Therefore, the required quadratic polynomial is αx² – (α + 1)x + 1.