TS EAMCET · Maths · Quadratic Equation

Let the transformed equation of $2 x^{4} - 8 x^{3} + 3 x^{2} - 1 = 0$ so that the term containing the cubic power of $x$ is absent be $2 x^{4} + b x^{2} + c x + d = 0$ . Then $b =$

A $- 18$
B $- 15$
C $- 9$
D $- 16$

Verified Solution

Answer & Solution

Correct Answer

(C) $- 9$

Step-by-step Solution

Detailed explanation

Given, The transformed equation of 2x4-8x3+3x2-1=0 so that the term containing the cubic power of x is absent be 2x4+bx2+cx+d=0, Now to find the transformed equation we will let x=y+h, So the equation 2x4-8x3+3x2-1=0 becomes, 2y+h4-8y+h3+3y+h2-1=0…

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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\(S_8\)	\(P_4\)	\(S_6\)	\(O_3\)
A	B	C	D

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Let the transformed equation of 2x4-8x3+3x2-1=0 so that the term containing the cubic power of x is absent be 2x4+bx2+cx+d=0. Then b=

Step-by-step Solution

Let the transformed equation of $2 x^{4} - 8 x^{3} + 3 x^{2} - 1 = 0$ so that the term containing the cubic power of $x$ is absent be $2 x^{4} + b x^{2} + c x + d = 0$ . Then $b =$