The equation $\displaystyle 2x^{2}+3x+1= 0$ has
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two rational roots.
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two irrational roots.
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integral roots.
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none of these
Reveal answer
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A
Correct answer
Explanation
Discriminant D = b^2 - 4ac = 3^2 - 4(2)(1) = 9 - 8 = 1. Since D > 0 and is a perfect square, the roots are rational and distinct.
AI explanation
To determine the nature of the roots, we use the discriminant formula D = b^2 - 4ac. For the equation 2x^2 + 3x + 1 = 0, the values are a = 2, b = 3, and c = 1. Calculating the discriminant gives 3^2 - 4(2)(1) = 9 - 8 = 1. Because the discriminant is 1, which is a perfect square, the equation has two rational roots.