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Question

If x is real, then the value of x23x+4x2+3x+4 lies in the interval

A
[13,3]
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B
[15,5]
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C
[16,6]
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D
[17,7]
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Solution

The correct option is B [17,7]

Let y =x23x+4x2+3x+4

(y1)x2+3(y+1)x+4(y1)=0

Since x is real , D0

9(y2+2y+1)16(y22y+1)0

7(y2+1)+50y0

7y250y+70

(7y1)(y7)0

y lies in [17,7]


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