Math, asked by aryananwariya1234, 9 months ago

Only a pro mathematician can solve this​

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Answered by UtsavPlayz
0

f(x) =  \sqrt{ {x}^{2}   -  3 |x| + 2 }

For finding roots. We equate it to 0

As there is Modulus we can split into 2 cases

 {x}^{2}  - 3x + 2 = 0 \\ and \\  {x}^{2}  + 3x + 2 = 0

After we find the roots we need to check the sol.

1. \:  {x}^{2}  - 2x - x + 2 = 0 \\ x(x - 2) - 1(x - 2) = 0 \\ (x - 2)(x - 1) = 0 \\ x - 2 = 0 \\ x = 2 \\ x - 1 = 0 \\ x = 1

2. \:  {x}^{2}  + 3x + 2 = 0 \\  {x}^{2}  + 2x + x + 2 = 0 \\ x(x + 2) + 1(x + 2) = 0 \\ (x + 2)(x + 1) = 0 \\ x  + 2 = 0 \\ x =  - 2 \\ x + 1 = 0 \\ x =  - 1

Now checking all Roots for f(x) = 0

 {x}^{2}  - 3 |x|  + 2 = 0

Now, As only the signs of the roots are changed so the modulus of -ve or +ve will just be +ve. Therfore the roots of f(x) = 0 Are 1, 2, -1. -2.

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Answered by bhanuprakashreddy23
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