AP EAMCET201922 Apr 2019Morning ShiftMathematicsQuadratic EquationActual

If (x R ) and (1 3 x^2-7 x+8 x^2+1 2 ), then the minimum and maximum values of (x ) are respectively.

Options

A1,2
B5,12
C6,10
D1, 6

Correct answer

D. 1, 6

Step-by-step solution

Given, (1 3 x^2-7 x+8 x^2+1 2 [ x^2+1 0 ] ) Now, ( 1 x^2-7 x+8 x^2+1 ) (0 2 x^2-7 x+7 ) ( f(x)=2 x^2-7 x+7 ) ( =(7)^2-4(2)(0) ) ( 0 ) ( x R ) and ( 3 x^2-7 x+8 x^2+1 2 ) ( x^2-7 x+6 0 ) ( (x-1)(x-6) 0 x [1,6] ) Hence, minimum and maximum values are 1 and 6.

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