-11
-9
-3
4
Correct answer is C
Using the remainder theorem, the remainder when a polynomial \(ax^{2} + bx + c\) is divided by \((x - a)\) is equal to \(f(a)\).
\(2x^{3} + 3x^{2} + qx - 1\) divided by \((x + 2)\), the remainder = \(f(-2)\)
\(\implies f(-2) = f(1)\)
\(f(-2) = 2(-2^{3}) + 3(-2^{2}) + q(-2) - 1 = -16 + 12 - 2q - 1 = -5 - 2q\)
\(f(1) = 2(1^{3}) + 3(1^{2}) + q(1) - 1 = 2 + 3 + q - 1 = 4 + q\)
\(4 + q = -5 -2q \implies 4 + 5 = -2q - q = -3q\)
\(q = -3\)
If the midpoint of the line joining (1 - k, -4) and (2, k + 1) is (-k, k), find the value of k. ...
Evaluate \(\cos 75°\), leaving the answer in surd form....
Evaluate \(\frac{\tan 120° + \tan 30°}{\tan 120° - \tan 60°}\)...
Evaluate \(\int_{-2}^{3} (3x^{2} - 2x - 12) \mathrm {d} x\)...
Given that \(p = \begin{bmatrix} x&4\\3&7\end{bmatrix} Q =\begin{bmatrix} x&3\\1&2x\...
A function \(f\) is defined by \(f :x→\frac{x + 2}{x - 3},x ≠ 3\).Find the inverse of \(f\)&...
Given that X : R \(\to\) R is defined by x = \(\frac{y + 1}{5 - y}\) , y \(\in\) R, find ...
If \(Px^{2} + (P+1)x + P = 0\) has equal roots, find the values of P....