AP EAMCET202315 May 2023Evening ShiftMathematicsQuadratic EquationActual

The minimum value of f(x)= x^2-2 x+3 x^2-4 x+7 is

Options

A1+ 1 3
B3- 3 3
C2- 1 3
D3- 1 3

Correct answer

B. 3- 3 3

Step-by-step solution

aligned & Given f(x)= x^2-2 x+3 x^2-4 x+7 =y & x^2-2 x+3=y x^2-4 x y+7 y & (y-1) x^2+(2-4 y) x+7 y-3=0 & (2-4 y)^2-4(y-1)(7 y-3) 0 (for real x ) & 1+4 y^2-4 y-7 y^2+10 y-3 0 & 3 y^2-6 y+2 0 1- 3 3 y 1+ 3 3 & y_ = 3- 3 3 aligned

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