Which of the following equations has two equal real roots?
- $2x^2-3\sqrt{2}x+\cfrac{9}{4}=0$
- $x^2 + x + 6 = 0$
- $x^2 + 3x + 2 \sqrt{2} = 0$
- $5x^2 + 3x + 1 = 0$
Reveal answer
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A
Correct answer
Explanation
For a quadratic equation to have equal real roots, the discriminant D = b^2 - 4ac must be zero. For 2x^2 - 3sqrt(2)x + 9/4 = 0, D = (-3sqrt(2))^2 - 4(2)(9/4) = 18 - 18 = 0.
AI explanation
A quadratic equation has two equal real roots when its discriminant (D = b^2 - 4ac) equals zero. For the equation 2x^2 - 3*(2^(1/2))x + 9/4 = 0, the values are a = 2, b = -3*(2^(1/2)), and c = 9/4. Calculating the discriminant gives (-3*(2^(1/2)))^2 - 4(2)(9/4), which simplifies to 18 - 18 = 0. Therefore, this equation has two equal real roots.