TS EAMCET · Maths · Quadratic Equation

If the roots of the equation $3 x^{3} - 26 x^{2} + 52 x - 24 = 0$ are in geometric progression, then the sum of two of its roots is

A $\frac{8}{3}$
B $\frac{10}{3}$
C $9$
D $10$

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{8}{3}$

Step-by-step Solution

Detailed explanation

Let, the roots of the equation 3x3-26x2+52x-24=0 are ar, a, ar. We know that, the sum and product of roots of the equation Ax3+Bx2+Cx+D=0 are respectively -BA and -DA. Hence, we have product of roots ar×a×ar=--243 ⇒a3=8 ⇒a=2. Now, the sum of the…

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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Column I		Column II
A)	For ring	I)	$\frac{M g \sin θ}{2.5}$
B)	For solid sphere	II)	$\frac{M g \sin θ}{3}$
C)	For solid cylinder	III)	$\frac{M g \sin θ}{3.5}$
D)	For hallow cylinder	IV)	$\frac{M g \sin θ}{2}$

If the roots of the equation 3x3-26x2+52x-24=0 are in geometric progression, then the sum of two of its roots is

Step-by-step Solution

If the roots of the equation $3 x^{3} - 26 x^{2} + 52 x - 24 = 0$ are in geometric progression, then the sum of two of its roots is