Form a quadratic polynomial whose zeroes are and ?

Question

Form a quadratic polynomial whose zeroes are  and  ?

Philoid · Accepted Answer

Let and be roots of the quadratic polynomial

The quadratic polynomial is given by x² – (α + β)x + αβ = 0…(1)

Let us Find α + β

⇒ α + β = 6 …(i)

Now lets Find αβ

Using identity (a + b)(a – b) = a² – b²

…(ii)

Putting values of (α + β) and αβ from (i) and (ii) in (1)

Multiplying throughout by 25

⇒ 25x² – 150x + 222 = 0

Hence the quadratic is 25x² – 150x + 222 = 0