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Question

If x is real, then the maximum and minimum values of expression x2+14x+9x2+2x+3will be


A

4, - 5

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B

5, - 4

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C

- 4, 5

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D

- 4, - 5

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Solution

The correct option is A

4, - 5


Let y=x2+14x+9x2+2x+3

y(x2+2x+3)x214x9=0

(y1)x2+(2y14)x+3y9=0

For real x, its discriminant ≥ 0

i.e. 4(y7)24(y1)3(y3)0

y2+y200 or (y4)(y+5)0

Now, the product of two factors is negative if these are of opposite signs. So following two cases arise:

Case 1: y40 or y4 y+50 or y5

This is not possible.

Case 2: y40 or y4 y+50 or y5 Both of these are satisfied if -5≤y≤4

hence maximum value of y is 4 and minimum value is -5


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