The roots of the equation ${2x^{2 }+ 3x + 2} = 0$ are
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Real, rational, and equal
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Real,rational and unequal
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Real, irrational, and unequal
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non real (imaginary)
Reveal answer
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D
Correct answer
Explanation
For the equation 2x^2 + 3x + 2 = 0, the discriminant D = b^2 - 4ac = 3^2 - 4(2)(2) = 9 - 16 = -7. Since the discriminant is negative, the roots are non-real (imaginary).
AI explanation
The nature of a quadratic equation's roots is determined by its discriminant, calculated as D equals b squared minus 4ac. Substituting the coefficients from 2x squared plus 3x plus 2 equals 0 gives D equals 3 squared minus 4 times 2 times 2, which simplifies to 9 minus 16, or negative 7. Since the discriminant is less than zero, the roots are non real (imaginary).