Multiple choice

State the nature of the given quadratic equation $2x^2 +6x + \cfrac{9}{2} = 0$

  1. Real and Distinct roots

  2. Real and equal roots

  3. Imaginary roots

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 2x^2 + 6x + 4.5 = 0, the discriminant D = b^2 - 4ac = 6^2 - 4(2)(4.5) = 36 - 36 = 0. Since D = 0, the roots are real and equal.

AI explanation

The nature of the roots is determined by the discriminant, calculated using the formula D = b^2 - 4ac. For the equation 2x^2 + 6x + 9/2 = 0, the coefficients are a = 2, b = 6, and c = 9/2. The discriminant is 6^2 - 4(2)(9/2), which simplifies to 36 - 36 = 0. Since the discriminant is zero, the equation has real and equal roots.

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