Multiple choice

The roots of the equation ax2 + x + b = 0 are equal if

  1. b2 = 4a

  2. b2 < 4a

  3. b2 > 4a

  4. ab = 1/4
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D Correct answer
Explanation

For the quadratic equation ax^2 + x + b = 0 to have equal roots, the discriminant D = b^2 - 4ac must be zero. Here, a=a, b=1, c=b. So 1^2 - 4(a)(b) = 0, which means 1 = 4ab, or ab = 1/4.

AI explanation

For the quadratic equation ax^2 + x + b = 0 to have equal roots, the discriminant (b^2 - 4ac) must equal zero. Here, the coefficient of x is 1, the constant term is b, and the leading coefficient is a, so we set 1^2 - 4(a)(b) = 0. This simplifies to 1 - 4ab = 0, which means ab = 1/4.

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