If α and β are the roots of 3x\(^2\) - 7x + 6 = 0, find \(\frac{1}{α}\) + \(\frac{1}{β}\)
\(\frac{7}{6}\)
\(\frac{7}{3}\)
\(\frac{14}{5}\)
\(\frac{14}{3}\)
Correct answer is A
3x\(^2\) - 7x + 6 = 0
α + β = \(\frac{7}{3}\);
αβ = 2;
\(\frac{1}{α}\) + \(\frac{1}{β}\) = \(\frac{α +β}{αβ}\)
\(\frac{7}{3}\) ÷ 2
= \(\frac{7}{6}\)
In how many ways can 8 persons be seated on a bench if only three seats are available?
100
125
336
427
Correct answer is C
\(^3{P}_3\) = \(\frac{8!}{8-3}!\)
= \(\frac{(8 * 7 * 6 * 5)!}{5!}\)
= 336
63.616
63.167
62.628
62.629
Correct answer is B
Put 1 + (0.998) = 1 + x;
x = (0.998)
Hence; 1 + 6(0.998) + 15(0.998)(0.998)\(^2\) + 20(0.998)\(^3\) + 15(0.998)\(^4\) + 6(0.998)\(^5\) + (0.998)\(^6\)
= 1 + 5.988 + 14.790 + 19.880 + 14.880 + 5.940 + 0.990
≈ 63.167
g(x) = 2x + 3 and f(x) = 3x\(^2\) - 2x + 4 find f {g (-3)}.
37
1
-3
-179
Correct answer is A
g(-3) = 2(-3) + 3 = -6 + 3 = -3
F(-3) = 3 (-3)\(^2\) - 2(-3) + 4
= 27 + 6 + 4 = 37
Solve (\(\frac{1}{9}\))\(^{x + 2}\) = 243\(^{x - 2}\)
\(\frac{7}{5}\)
\(\frac{6}{7}\)
\(\frac{-7}{6}\)
\(\frac{-6}{7}\)
Correct answer is A
(\(\frac{1}{9}\))\(^{x + 2}\) = 243\(^{x - 2}\)
3\(^{-2(x + 2)}\) = 3\(^{5(x - 2)}\);
-2(x+2) = 5(x - 2)
-2x -4 = 5x - 10
-7x = -6
x = \(\frac{6}{7}\)