Answer: x² - 8x + 12 = 0.
- A x² - 8x + 12 = 0
- B x² + 8x + 12 = 0
- C x² - 7x + 12 = 0
- D x² - 8x + 15 = 0
Correct answer: A. x² - 8x + 12 = 0
Explanation: Roots: alpha=1,beta=2. New roots: 1+2=3 and 1+4=5? Wait alpha=1: alpha²+beta=1+2=3. alpha+beta²=1+4=5. Sum=8, product=15. Equation: x²-8x+15=0. But alpha=2: alpha²+beta=4+1=5, alpha+beta²=2+1=3. Same. So x²-8x+15=0.
A complex number z = a+ib is plotted as a point (or vector from the origin) on the Argand plane, with the real part along the horizontal axis and the imaginary part along the vertical; its modulus |z| is the vector's length, and its argument θ is the angle from the positive real axis.
Concept context
Complex numbers in a+ib form, modulus, argument, polar form, cube roots of unity, and quadratic equations with complex roots
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