MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Sigma n

If the equati...

Question

If the equation $x^{2} + a x + b = 0$ and $x^{2} + b x + a = 0$ have a common root, then the numerical value of a+b is $- 1$ .( Enter 1 if true or 0 otherwise)

Open in App

Solution

$α^{2} + a α + b = 0,$
$α^{2} + b α + a = 0$
Subtracting, $α (a - b) - (a - b) = 0 \Rightarrow α - 1 = 0$
Putting $α = 1$ in one of the above equation we have , $1 + a + b = 0$
$∴ a + b = - 1$

Suggest Corrections

thumbs-up

0

Similar questions

Q. If every pair of equations

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

has a common root, then product of these common roots

α β γ = a b c

.( Enter 1 if true or 0 otherwise)

Q. If the equations

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

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

have exactly one common root, then the numerical value of

a + b

Q. If the quadratic equation

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

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

have a common root, then find the numerical value of

a + b

a \neq b,

if the equations

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

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

have a common root, the value of

(a + b)

Q. If one of the roots of the equation

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

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

is coincident, then the numerical value of

(a + b)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Summation by Sigma Method

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon