Find the roots of quadratic equations 9x^2 - 9(a + b)x + (2a^2 + 5ab + 2b^2) = 0

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Find the roots of quadratic equations 9x2 - 9(a + b)x + (2a2 + 5ab + 2b2) = 0

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We write -9(a + b)x = -3(2a + b)x - 3(a + 2b)x as

⇒ x = $\cfrac{2a+b}3$ or x = $\cfrac{a+2b}3$

Hence, $\cfrac{2a+b}3$ and $\cfrac{a+2b}3$ are the roots of the given equation.