A root of equation ax2 bx c 0 where a b and c are rational numbers is 5 3 radic 3 What is the value ...........

Quantitative Aptitude ( CCS) Quadratic Equations

A root of equation ax² + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a² + b²+ c²) / (a + b + c)?

-105/11

105/11

11/105

-11/105

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Explanation:

Since one root of the equation is irrational, so another root will be 5 – 3√3
According to the problem statement,
⇒ [x – (5 + 3√3)] [x – (5 – 3√3)] = 0
⇒ x² – 10x – 2 = 0
⇒ a = 1, b = -10 and c = -2, Put this in the required equations
∴ (a² + b² + c²) / (a + b + c) = (1 + 100 + 4) / (1 – 10 – 2) = -105/11