3 years ago

Can a quadratic have one real and one non real root

1 answer:

3 0

Answer:

Yes, it is possible. We already know that complex roots exist in conjugate pair but the case is true only when the equation has real coefficients. But on the other hand, if the equation has complex coefficients, then it is possible to attain one real and one complex root.

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Write a polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

kogti [31]

9514 1404 393

Answer:

f(x) = x³ -5x² +2x +8

Step-by-step explanation:

If the function has a zero of p, then it has a factor of (x-p). The polynomial of least degree will only have factors corresponding to the given zeros:

f(x) = (x -(-1))(x -2)(x -4)

= (x +1)(x -2)(x -4)

= (x² -x -2)(x -4)

f(x) = x³ -5x² +2x +8