Question

Only a pro mathematician can solve this​

Answer 1

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

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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Answer 2

Answer:

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