Question

If the polynomial $$p(x) = x^3 - 4kx + 3$$ is divided by $$(2x + 1)$$, then the remainder obtained is –3. The value of $$k$$ is ______.

Options

• $$-\frac{17}{16}$$

• $$-\frac{47}{8}$$

• $$-\frac{27}{16}$$

• $$-\frac{47}{16}$$

Answer 1

If the polynomial $$p(x) = x^3 - 4kx + 3$$ is divided by $$(2x + 1)$$, then the remainder obtained is –3. The value of $$k$$ is `underlinebb(-47/16)`.

Explanation:

$$f(-\frac{1}{2}) = 2k + 3 -\frac18 = -3$$, so $$k = -\frac{47}{16}$$.