TS EAMCET · Maths · Quadratic Equation

If $\frac{α}{α + 1}$ and $\frac{β}{β + 1}$ are the roots of the quadratic equation $x^{2} + 7 x + 3 = 0,$ then the equation having roots $α$ and $β$ is

A $3 x^{2} - x - 3 = 0$
B $11 x^{2} + 13 x + 3 = 0$
C $13 x^{2} + 11 x + 13 = 0$
D $11 x^{2} + 3 x + 13 = 0$

Verified Solution

Answer & Solution

Correct Answer

(B) $11 x^{2} + 13 x + 3 = 0$

Step-by-step Solution

Detailed explanation

The equation having roots as α and β will be x2-(α+β)x+αβ=0 Which can be written as 1αβx2-(α+βαβ)x+1=0 ⇒1αβx2-(1α+1β)x+1=0 Now from given…

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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If αα+1 and ββ+1 are the roots of the quadratic equation x2+7x+3=0, then the equation having roots α and β is

Step-by-step Solution

If $\frac{α}{α + 1}$ and $\frac{β}{β + 1}$ are the roots of the quadratic equation $x^{2} + 7 x + 3 = 0,$ then the equation having roots $α$ and $β$ is