Question : If the sum of the roots of a quadratic equation is 1 and the product of the roots is –20, find the quadratic equation.

Option 1: $x^{2}–x–20=0$

Option 2: $x^{2}+x+20=0$

Option 3: $x^{2}+x–20=0$

Option 4: $x^{2}–x+20=0$

Question : The sum of a non-zero number and twice its reciprocal is $\frac{33}{4}$. Find the number.

Option 1: 9

Option 2: 10

Option 3: 11

Option 4: 8

Question : A number is greater than 58 times its reciprocal by $\frac{3}{4}$. What is the number?

Option 1: –8

Option 2: 12

Option 3: –12

Option 4: 8

Question : If $(a+\frac{1}{a})=–2$, then the value of $a^{1000}+a^{–1000}$ is:

Option 1: $2$

Option 2: $0$

Option 3: $1$

Option 4: $\frac{1}{2}$

Question : If $a+\frac{1}{a}=1$, then the value of $\frac{a^2-a+1}{a^2+a+1}$ is $(a\neq 0)$:

Option 1: 1

Option 2: –1

Option 3: 0

Option 4: 2