-6, -1
6, 1
1, -1
6, -6
Correct answer is A
\(x^{3} + px^{2} + qx + 6 = 0\)
f(x - 1) = 0; f(1) = 0.
\(1^{3} + p(1^{2}) + q(1) + 6 = 0 \implies p + q = -7 ... (1)\)
f(x + 1) = 0; f(-1) = 0.
\((-1)^{3} + p(-1^{2}) + q(-1) + 6 = 0 \implies p - q = -5 ... (2)\)
Subtract (2) from (1).
\(2q = -2 \implies q = -1\)
\(p - (-1) = -5 \implies p = -5 - 1 = -6\)
\((p, q) = (-6, -1)\)
If S = (x : x\(^2\) = 9, x > 4), then S is equal to
4
{0}
\(\emptyset\)
{\(\emptyset\)}
Correct answer is C
No explanation has been provided for this answer.
25
21
16
3
Correct answer is B
Number of people playing both rugby and cricket = 4 Number that play cricket only = 11 - 4 = 7 Number that play rugby only = 14 - 4 = 10. Number that play for at least one of the teams = 4 + 7 + 10 = 21.
Simplify \(\frac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}}\)
\(\frac{1}{3}\)
9
16cm
3
Correct answer is A
\(\frac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}}\)
\(\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}\)
\(\therefore \frac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}} = \frac{2\sqrt{3} - \sqrt{3}}{2\sqrt{3} + \sqrt{3}}\)
= \(\frac{\sqrt{3}}{3\sqrt{3}}\)
= \(\frac{1}{3}\)
Evaluate \(\frac{(81)^{\frac{3}{4}} - (27)^{\frac{1}{3}}}{3 \times 2^3}\)
27
1
\(\frac{1}{3}\)
\(\frac{1}{8}\)
Correct answer is B
\(\frac{(81)^{\frac{3}{4}} - (27)^{\frac{1}{3}}}{3 \times 2^3}\)
= \(\frac{(3^{4})^{\frac{3}{4}} - (3^{3})^{\frac{1}{3}}}{3 \times 2^{3}}\)
= \(\frac{3^{3} - 3^{1}}{24}\)
= \(\frac{27 - 3}{24} = 1\)