Equation - Quadratic Equation

SOURCE:COMPETITION
Number of Problems: 11. : (Book)

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Real numbers $x$ and $y$ satisfy the equation $x^2 + y^2 = 10x - 6y - 34$ . What is $x + y$ ?

$extbf{(A)} 1 qquad extbf{(B)} 2 qquad extbf{(C)} 3 qquad extbf{(D)} 6 qquad extbf{(E)} 8$

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7.

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For which of the following values of $k$ does the equation $frac{x-1}{x-2} = frac{x-k}{x-6}$ have no solution for $x$ ?

$extbf{(A) } 1qquad extbf{(B) } 2qquad extbf{(C) } 3qquad extbf{(D) } 4qquad extbf{(E) } 5$

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8.

'Let $d$ and $e$ denote the solutions of $2x^{2}+3x-5=0$ . What is the value of $(d-1)(e-1)$ ?

$mathrm{(A) } -frac{5}{2}qquad mathrm{(B) } 0qquad mathrm{(C) } 3qquad mathrm{(D) } 5qquad mathrm{(E) } 6$

9.

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Two different positive numbers $a$ and $b$ each differ from their reciprocals by $1$ . What is $a+b$ ?

$ext{(A) }1qquad ext{(B) }2qquad ext{(C) }sqrt 5qquad ext{(D) }sqrt 6qquad ext{(E) }3$

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10.

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The quadratic equation $x^2+mx+n$ has roots twice those of $x^2+px+m$ , and none of $m,n,$ and $p$ is zero. What is the value of $n/p$ ?

$mathrm{(A)} {{{1}}} qquad mathrm{(B)} {{{2}}} qquad mathrm{(C)} {{{4}}} qquad mathrm{(D)} {{{8}}} qquad mathrm{(...$

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11.

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There are two values of $a$ for which the equation $4x^2 + ax + 8x + 9 = 0$ has only one solution for $x$ . What is the sum of those values of $a$ ?

$mathrm{(A) } -16qquad mathrm{(B) } -8qquad mathrm{(C) } 0qquad mathrm{(D) } 8qquad mathrm{(E) } 20$

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