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Right Hand Limit

If equation ...

Question

If equation $x^{2} + a x + b c = 0$ and $x^{2} + b x + c a = 0$ have one root common then their remaining roots are-

A

a, b

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B

a, c

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C

b, c

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D

none of these

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Solution

The correct option is A $a, b$
$x^{2} + a x + b x = 0 x^{2} + b x + c a = 0 l e t c o m m o n r o o t b e t ∴ t^{2} + a t + b c = 0 - e q 1 t^{2} + b t + a c = 0 - e q 2 e q 1 - 2 a t - b t + b c - a c = 0 t (a - b) = c (a - b) t = c ∴ c^{2} + a c + b c = 0 a + b + c = 0 ∴ r e m a i n i n g r o o t s a r e a & b$

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Similar questions

Q. If the equations

x^{2} + a x + b c = 0

x^{2} + b x + c a = 0

have a common root and if

a, b

c

are non-zero distinct real numbers, then their other roots satisfy the equation :

Q. Assertion :If the equation

x^{2} + b x + c a = 0

x^{2} + c x + a b = 0

have a common root, then their other root will satisfy the equation

x^{2} + a x + b c = 0

Reason: If the equation

x^{2} = b x + c a = 0

x^{2} + c x + a b = 0

have a common root, then

a + b + c = 0

x^{2} + a x + b c = 0

x^{2} + b x + c a = 0

(c \neq 0)

have a common root. Then other root satisfies the equation

x^{2} + a x + b c = 0

x^{2} + b x + c a = 0 (a \neq b)

have a common root, then prove that their other roots satisfy the equation

x^{2} + c x + a b = 0

x^{2} + a x + b c = 0,

x^{2} + b x + a c = 0,

a \neq b

have one root in common, then their other roots satisfy the equation

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