If each root of the equation $x^{2} + 11 x + 13 = 0$ is diminished by $4$ , then the resulting equation is

x^{2} + 3 x - 15 = 0

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x^{2} + 3 x + 73 = 0

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x^{2} + 19 x + 73 = 0

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x^{2} - 3 x - 4 = 0

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Solution

The correct option is C $x^{2} + 19 x + 73 = 0$
$T h e r o o t s o f t h e e q u a t i o n x^{2} + 11 x + 13 = 0 i s d i m i n i s h e d b y 4 i . e . t h e v a r i a b l e b e c o m e s (x + 4) . ∴ T h e n e w e q u a t i o n i s (x + 4)^{2} + 11 (x + 4) + 13 = 0 \Rightarrow x^{2} + 8 x + 16 + 11 x + 44 + 13 = 0 \Rightarrow x^{2} + 19 x + 73 = 0 A n s - O p t i o n C .$

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