Quadratic Formula for Finding Roots

Q. The value of $\sqrt{8+2\sqrt{8+2\sqrt{8+2\sqrt{8+...\infty }}}}$ is

1. $6$
2. $-2$ and $4$
3. $4$
4. $8$

Q.

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

1. None of these

2. 

3. 

4. 

Q.

If a > 0, then $\sqrt{\{a+\sqrt{(a+....)}\}}$=

1. 

2. 

3. 

4. None of these

Q. Solve the equation

Q.

If $\alpha ,\beta and\gamma$ are the roots of the equation $x^3+2x^2+3x+1=0$ . Find the equation whose roots are ${\alpha }^3$, ${\beta }^3$ and ${\gamma }^3$.

1. 

2. 

3. 

4. 

Q. Solve the equation

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

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

Q. Solve the equation

Q. 8. 3x2x 330

Q. 3, x2 + 3x + 9 = 0

Q. Solve the equation 27 x 2 – 10 x + 1 = 0

Q. 6, x2-x + 2 = 0

Q. 1.x2 + 3 = 0

Q. 5, x2 + 3x + 5 = 0

Q.

Sum of the roots of an equation, $4^x-3\left(2^{x+3}\right)+128=0$, is:

1. $0$

2. $7$

3. $5$

4. $8$

Q. The set of values of $a$ for which the function $f\left(x\right)=\frac{a{x}^3}{3}+(a+2)x^2+(a-1)x+2$ possesses a negative point of inflection is

1. $(-\infty ,-2)\cup (0,\infty )$
2. $(-2,0)$
3. $\varphi$
4. $\{-4,5\}$

Q. 2, 2x2 + x + 1 = 0

Q. 4.-x2 + x-2=0

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. Let $-\frac{\pi }{6}<\theta <-\frac{\pi }{12}$. Suppose ${\alpha }_1$ and ${\beta }_1$ are the roots of the equation $x^2-2x\sec \theta +1=0$ and ${\alpha }_2$ and ${\beta }_2$ are the roots of the equation $x^2+2x\tan \theta -1=0$. If ${\alpha }_1>{\beta }_1$ and ${\alpha }_2>{\beta }_2$, then ${\alpha }_1+{\beta }_2$ equals:

1. $2(\sec \theta -\tan \theta )$
2. $2\sec \theta$
3. $-2\tan \theta$
4. $0$

Q.

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

1. $\frac{b\pm \sqrt{b^2-4ac}}{2a}$

2. $\frac{-b\pm \sqrt{b^2-ac}}{2a}$

3. $\frac{2c}{-b\pm \sqrt{b^2-4ac}}$

4. None of these

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. $x^2-x-1=0$
2. $x^2-x+1=0$
3. $x^2+x-1=0$
4. $x^2+x+1=0$