If $A, B$ are roots of the quadratic equation $x^{2} - 5 x + 6 = 0$ then the equation whose roots are $A + 3$ and $B + 3$ is-

x^{2} - 11 x + 30 = 0

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(x - 3)^{2} - 5 (x - 3) + 6 = 0

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Both

(A)

and

(B)

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none of these

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Solution

The correct option is C Both $(A)$ and $(B)$
$ x^{2} - 5 x + 6 = 0 r o o t s a r e A, B s u m o f r o o t s = A + B = 5 p r o d u c t o f r o o t s = A B = 6 n e w r o o t s a r e (A + 3) & (B + 3) s u m = A + 3 + B + 3 = 5 + 6 = 11 p r o d u c t = (A + 3) (B + 3) = A B + 3 (A + B) + 9 = 6 + 15 + 9 = 30 e q u a t i o n : x^{2} - (s u m o f r o o t s) x + (p r o d u c t o f r o o t s) = 0 x^{2} - 11 x + 30 = 0$
After simply B also we will get same equation

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