If equation X square + bx + ca is equals to zero and X square + c X + ab is equals to zero have a non zero common root prove that a + b + c is equals to zero and their other Roots satisfy X square + a x + b c = 0

Open in App

Solution

Suggest Corrections

Similar questions

Q. If the equations

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

and

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

have a common root and if

a, b

and

c

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

Q. If equations

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

and

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

have only one non-zero common root, then find the equation for which other roots must satisfy.

If $a x^{2} + b x + c = 0 a n d b x^{2} + c x + a = 0$ have a common root and a,b,c are non - zero real numbers then $\frac{a^{3} + b^{3} + c^{3}}{a b c}$ is equal to :

Q. If

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

and

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

Q. Assertion :If the equation

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

and

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

and

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

have a common root, then

a + b + c = 0

Join BYJU'S Learning Program