A Simple Quadratic Transformation Using Vieta’s Formula

Can you find the quadratic equation whose roots are

1/(2a + b)  and  1/(6a + b),

given that 2 and 6 are the roots of

ax² + bx + 1 = 0?

A neat application of Vieta’s formulas leads to the answer without solving the original quadratic directly.

Question for discussion:
What is the required quadratic equation?

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