AP EAMCET · Maths · Quadratic Equation

For $a \neq b$ , if the equation $x^{2} + a x + b = 0$ and $x^{2} + b x + a = 0$ have a common root, then the value of $a + b =$

A $- 1$
B $0$
C $1$
D $2$

Verified Solution

Answer & Solution

Correct Answer

(A) $- 1$

Step-by-step Solution

Detailed explanation

Given: x2+ax+b=0 & x2+bx+a=0 Here, we can see that for x=1 both the equations are giving same expression, which is, 1+a+b=0 ⇒a+b=-1

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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For a≠b, if the equation x2+ax+b=0 and x2+bx+a=0 have a common root, then the value of a+b=

Step-by-step Solution

For $a \neq b$ , if the equation $x^{2} + a x + b = 0$ and $x^{2} + b x + a = 0$ have a common root, then the value of $a + b =$