AP EAMCET2001MathematicsQuadratic Equation

The minimum value of (x- )(x- ) is

Options

A0
B1 4 ( - )^2
C- 1 4 ( - )^2

Correct answer

Step-by-step solution

Let y=(x- )(x- ) aligned y & =x^2-( + ) x+ y^ & =2 x-( + ) aligned For maximum or minimum, put y^ =0 array rrrl & 2 x-( + ) & =0 & x & = + 2 & y^ & =2=+ ve array The minimum value at x= + 2 is aligned y & = ( + 2 - ) ( + 2 - ) & = 1 4 ( - )( - )=- 1 4 ( - )^2 aligned

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