Comparing the given equation with ax² + bx + c = 0, we get,

a= 2, b = –9 and c = 35

Then,

b² – 4ac = (–9)² – 4.2.35

= 81 – 280

= –199

Here, b² - 4ac < 0

So, the roots are imaginary and unequal.

Solⁿ:

Let α be the common root of the given equations:

α2 + pα + q = 0 …(i)

and α2 + p’α + q’ = 0 …(ii)

Solving (i) and (ii) by cross multiplication,

1 p q 1

1 p’ q’ 1

Or, α²/(pq′p′q) = α/(qq′) = 1/(p′p)

Then,

α²/(pq′p′q) = α/(qq′) or, α/(qq′) = 1/(p′p)

α = (pq′p′q)/(qq′) or, α = (qq′)/(p′p)

So, α be either (pq′p′q)/(qq′) or. (qq′)/(p′p)