Multiple choice

If the equations $x^2-3x+4=0$ and $x(b-3x)+2x+a=0$ have a common root then the absolute value of (a+b) is equal to

  1. 24

  2. 5

  3. 1

  4. None of these
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D Correct answer
AI explanation

The first equation, x^2 - 3x + 4 = 0, has a discriminant of 9 - 16 = -7, which is less than zero. This means the roots of the first equation are complex numbers. The second equation can be written as -3x^2 + (b + 2)x + a = 0, which has real coefficients a and b. Since a quadratic equation with real coefficients cannot have exactly one complex root in common with another real-coefficient equation, there are no real values for a and b that satisfy the condition. Therefore, the absolute value of a + b cannot be determined from the given options.

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