Question

Find the roots for the above given quadratic equation. Please show the working too.

Answer 1

Step-by-step explanation:

$9x^{2} - 9 (a + b)x + 2a^{2} + 5ab + 2b^{2} = 0\\9x^{2} - 3[(3a + 3b)]x + 2a^{2} + 4ab +ab + 2b^{2} = 0\\9x^{2} - 3[(a + 2b) + (2a + b)]x + 2a[a + 2b] + b [a + 2b] = 0\\9x^{2} - 3(a + 2b)x - 3 (2a + b) + (a + 2b)(2a + b) = 0\\3x [3x - (a + 2b)] -(2a + b)[3x - (a + 2b)]=0\\\:\: [3x - (a + 2b)] - [3x - (2a + b)] = 0\\\\\\\\\circ\:3x - (2a + b) = 0\\\boxed{\underline{x = \frac{2a + b}{3} }}\\\\\\\\\circ\:3x - (2a + b) = 0\\\boxed{\underline{x = \frac{a + 2b}{3} }}$

So, the roots are:

1) x = 2a + b/3

2) x = a + 2b/3

_________

Hope it helps!

◇ Please refer to the attachment if the latex code shows some error.

$\mathfrak{Lucazz}$

Answer 2

Look at the attachment.

Hope it helps ⚜