AP EAMCET202317 May 2023Evening ShiftMathematicsQuadratic EquationActual

For x R , the minimum value of x^2+2 x+5 x^2+4 x+10 is

Options

A1 2
B4 3
C3 4
D- 1 2

Correct answer

A. 1 2

Step-by-step solution

Let x^2+2 x+5 x^2+4 x+10 =y, y R aligned & x^2+2 x+5=y (x^2+4 x+10 ) & (y-1) x^2+(4 y-2) x+(10 y-5)=0 aligned Since, x R aligned & (4 y-2)^2-4(y-1)(10 y-5)>0 & 6 y^2-11 y+4 0 & (2 y-1)(3 y-4) 0 & y ( 1 2 , 4 3 ) aligned Minimum value of x^2+2 x+5 x^2+4 x+10 is 1 2

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