AP EAMCET202318 May 2023Morning ShiftMathematicsQuadratic EquationActual

The value of 4 x^3-4 x^2-7 x+127 when x= 4+5 -1 2 is

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Correct answer

D. 4

Step-by-step solution

x= 4+5 -1 2 2 x=4+5 -1 ...(i) (2 x)^2=(4+5 -1 )^2 4 x^2=16-25+40 -1 4 x^2=-9+40 -1 ...(ii) Equation (ii) -8 (i) 4 x^2-16 x=-41 4 x^2-16 x+41=0 ...(iii) Now, 4 x^3-4 x^2-7 x+127=x 4 x^2-4 x^2-7 x+127=x(16 x-41)-4 x^2-7 x+127 from (iii) aligned & =12 x^2-48 x+127 & =3 (4 x^2-16 x )+127 aligned =4

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