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Roots of Quadratic Equation

if the equati...

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if the equations x^2+abx+c=0 and x^2+acx+b=0 have a common root the teir other roots satisfy the equati

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Q. If the quadratic equations

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

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

have a common root, the equation containing their other roots is/are:

\begin{matrix} x^{2} + a b x + c = 0 x^{2} + a c x + b = 0 \end{matrix}}

one common root

α

.
Find the quadratic equation containing their common root

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

Q. If the equations

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

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

have a common root, show that

a + b + c = 0

also show that their other roots are and their other root are given by the equation

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

b \neq c

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

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