Write the number of real roots of the equation x2 + 3 |x| + 2 = 0.

1.	Write the number of real roots of the equation x2 + 3 \|x\| + 2 = 0.
Answer» If ax² + bx + c = 0 then x \(=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) If D = b² − 4ac ≥ 0 then the values of x are real If D = b² − 4ac < 0 then the values of x are complex \|z\| is always a positive real number regardless of x being a real number or complex number. Given eqn. is \|x\|² + 3\|x\| + 2 = 0 and a = 1, b = 3 and c = 2 \|x\|² + 3\|x\| + 2 = 0 ⇒ \|x\| = \(\frac{-3\pm\sqrt{9-8}}{2}\) ⇒ \|x\| = 2 or −1 But \|x\| cannot be negative No real root for the equation.

Answer»

If ax² + bx + c = 0 then x \(=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

If D = b² − 4ac ≥ 0 then the values of x are real

If D = b² − 4ac < 0 then the values of x are complex

|z| is always a positive real number regardless of x being a real number or complex number.

Given eqn. is |x|² + 3|x| + 2 = 0 and a = 1, b = 3 and c = 2

|x|² + 3|x| + 2 = 0

⇒ |x| = \(\frac{-3\pm\sqrt{9-8}}{2}\)

⇒ |x| = 2 or −1

But |x| cannot be negative

No real root for the equation.

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