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in Quadratic Equations by (31.2k points)
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Write the number of real roots of the equation x2 + 3 |x| + 2 = 0.

1 Answer

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Best 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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