Answer :

Let and be roots of the quadratic polynomial

The quadratic polynomial is given by x^{2} – (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) = a^{2} – b^{2}

…(ii)

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

Multiplying throughout by 25

⇒ 25x^{2} – 150x + 222 = 0

Hence the quadratic is 25x^{2} – 150x + 222 = 0

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