Multiple choice

The equation $(x-705)(x-795)+800(x-750)(x-835)=0$ has

  1. Imaginary roots

  2. Equal roots

  3. Distinct real roots

  4. None of these
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A Correct answer
AI explanation

To determine the nature of the roots, we can evaluate the discriminant, b^2 - 4ac. Letting y = x - 750, the equation becomes (y + 45)(y - 45) + 800y(y + 85) = 0, which simplifies to 801y^2 + 68000y - 2025 = 0. The discriminant is (68000)^2 - 4(801)(-2025), which evaluates to a large negative number. Since the discriminant is less than zero, the equation has imaginary roots.

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