Question

If the equation x^2 + ax + b and x^2 + bc + a have a common root then a + b = ,?

(a) –1 (b) 2 (c) 3 (d) 4​

Answer 1

Question:-

⇒ If the equation x^2 + ax + b and x^2 + bc + a have a common root then a + b = ,?

Answer:-

⇒ Let α be the common root then ,

we have given equation  :-

→ $x^2 + ax + b = 0$----(1)

→ $x^2 + bc + a = 0$----(2)

_-_-_-_-_-_-_-_-_-_-_-_-_

⇒ from equation (1)

 → $\alpha ^2 + a\alpha + b = 0$-----(3)

⇒ from equation (2)

 → $\alpha ^2 + b\alpha + a = 0$----(4)

_-_-_-_-_-_-_-_-_-_-_-_-_

therefore : equation (4) - (3)

we get

⇒ $\alpha ^2 + b\alpha + a - \alpha ^2 - a\alpha -b = 0$

⇒ $\alpha (b-a) + (a-b) = 0$

⇒ $\alpha (b-a) = - (a-b)$

⇒ $\alpha = \frac{-(a-b)}{b-a}$

⇒ $\alpha = 1$

so , 1 is common difference between them

by putting this value in equation ( 1)

We get .

⇒ $(1)^2 + a(1) + b = 0$

⇒ $a+ b = -1$

hence our option is (a)

which is correct option:)