Question

Find the roots for the above given quadratic equation.

Please show the working too.

Answer 1

Look at the attachment.

Hope it helps ⚜

Answer 2

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 = (2a + b)/(3) }}\\\\\\\\\circ\:3x - (2a + b) = 0\\\boxed{\underline{x = (a + 2b)/(3) }}`

So, the roots are:

1) x = 2a + b/3

2) x = a + 2b/3

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Hope it helps!

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

`\mathfrak{Lucazz}`