Multiple choice

Determine the nature of the roots of the given equation from their discriminants. $2x^{2}\, -\, 7x\, -\, 3\, =\, 0$

  1. Real and unequal

  2. Real and equal

  3. One real and one imaginary

  4. Both imaginary
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A Correct answer
Explanation

The discriminant D = b^2 - 4ac. For 2x^2 - 7x - 3 = 0, a=2, b=-7, c=-3. D = (-7)^2 - 4(2)(-3) = 49 + 24 = 73. Since D > 0 and not a perfect square, the roots are real and unequal.

AI explanation

Use the discriminant formula D equals b squared minus 4ac. For the equation 2x squared minus 7x minus 3 equals 0, D equals (-7) squared minus 4 times 2 times -3, which is 49 plus 24, totaling 73. Because 73 is greater than zero, the roots are real and unequal.

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