Quadratic Formula for Finding Roots

Q. The number of solutions of : $lo{g}_4(x-1)=lo{g}_2(x-2)$ is

1. 3
2. 1
3. 2
4. 0

Q.

If $a{x}^2+bx+c=0$, then x =

1. 

2. 

3. 

4. None of these

Q. The value of $2+\frac{1}{2+\frac{1}{2+.....\infty }}$ is

1. 
2. 
3. None of these
4. 

Q. Let $\alpha$ and $\beta$ be the roots of the equation $x^2+x+1=0$. The equation whose roots are ${\alpha }^{19},{\beta }^7$ is

1. x² - x - 1 = 0
2. x² + x - 1 = 0
3. x² + x + 1 = 0
4. x² - x + 1 = 0

Q. If x = $\sqrt{1+\sqrt{1+\sqrt{1+.....toinfinity}}},$ then x =

1. 
2. 
3. None of these
4. 

Q.

The number of real roots of the equation $e^{sinx}-e^{-sinx}-4=0$ are

1. 1

2. 2

3. Infinite

4. 0

Q. Let $\alpha$ and $\beta$ be the roots of equation $x^2-6x-2=0$ . If $a_n={\alpha }^n{\beta }^n$, for $n\le 1$, then the value of $\frac{a_{10}-2a_8}{2a_9}$ is equal to :

1. -6
2. 3
3. 6
4. -3

Q. if $\alpha ,\beta$ are the roots of the equation $x^2-x+1=0$, then ${\alpha }^{2009}+{\beta }^{2009}$ =

1. 1
2. -1
3. 2
4. -2

Q. The sum of all real values of x satisfying the equation $(x^2-5x+5{)}^{x^2+4x-60}=1$ is :

1. 5
2. 6
3. 3
4. -4

Q. The equation $e^{sinx}-e^{-sinx}-4=0$ has:

1. exactly one real root
2. exactly four real roots
3. infinite number of real roots
4. no real roots