What must be added to the expression x\(^2\) - 18x to make it a perfect square?
3
9
36
72
81
Correct answer is E
x\(^2\) - 18x to be a perfect square.
\((\frac{b}{2})^2\) is added to ax\(^2\) + bx + c in order to make it a perfect square.
\(x^2 - 18x + (\frac{-18}{2})^2\)
= \(x^2 - 18x + 81\)
Write as a single fraction \(\frac{1}{1 - x} + \frac{2}{1 + x}\)
\(\frac{x + 3}{1 - x^2}\)
\(\frac{3 - x}{(1 - x)^2}\)
\(\frac{3 - x}{1 + x^2}\)
\(\frac{3 - x}{(1 + x)^2}\)
\(\frac{3 - x}{1 - x^2}\)
Correct answer is E
\(\frac{1}{1 - x} + \frac{2}{1 + x}\)
= \(\frac{(1 + x) + 2(1 - x)}{(1 - x)(1 + x)}\)
= \(\frac{1 + x + 2 - 2x}{1 - x^2}\)
= \(\frac{3 - x}{1 - x^2}\)
Construct a quadratic equation whose roots are \(-\frac{1}{2}\) and 2.
3x2-3x+2=0
3x2+3x-2=0
2x2+3x-2=0
2x2-3x+2=0
2x2-3x-2=0
Correct answer is E
If x = \(-\frac{1}{2}\) and 2; then
\(x + \frac{1}{2} = 0\) and \(x - 2 = 0\)
\(\implies (x + \frac{1}{2})(x - 2) = 0\)
\(x^2 - 2x + \frac{1}{2}x - 1 = 0\)
\(x^2 - \frac{3}{2}x - 1 = 0\)
\(2x^2 - 3x - 2 = 0\)
Factorize the expression 2y\(^2\) + xy - 3x\(^2\)
2y (y + x) - 3x2
(2y - x)(2y + x)
(3x - 2y(x - y)
(2y + 3x)(y - x)
(x – y)(2y + 3x)
Correct answer is D
2y\(^2\) + xy - 3x\(^2\)
2y\(^2\) + 3xy - 2xy - 3x\(^2\)
y(2y + 3x) - x(2y + 3x)
= (y - x)(2y + 3x)
Evaluate \(\log_{10} 25 + \log_{10} 32 - \log_{10} 8\)
0.2
2
100
409
490
Correct answer is B
\(\log_{10} 25 + \log_{10} 32 - \log_{10} 8\)
= \(\log_{10} (\frac{25 \times 32}{8})\)
= \(\log_{10} 100 \)
= 2