Solving Using Quadratic Formula When D>0

Q. If $\alpha$, $\beta$ are the roots of the equation $x^2-5x+6=0$, then the value of ${\alpha }^2-{\beta }^2$ is:

1. $\pm 5$
2. $\pm 13$
3. $\pm 6$
4. $\pm 7$

Q.

What is sridharacharya method?

Q. If $x=\frac{1}{(2-\sqrt{3}),}$ then find the value of $(x^2-4x+1)$.

Q.

The roots of the equation $x^3-3x-2=0$ are:

1. $-1,-1,2$

2. $-1,1,-2$

3. $-1,2,-3$

4. $-1,-1,-2$

Q. Find the roots of the quadratic equation $a{x}^2+bx+c=0$.

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

Q. Solve for $2(x^2+\frac{1}{x^2})-9(x+\frac{1}{x})+14=0$

1. $\frac{1}{2},1,2$
2. $\frac{1}{2},1,-4$
3. $\frac{1}{2},1,-2$
4. $\frac{1}{2},1,4$

Q. Find the roots of the equations :
$x+\frac{1}{x}=3,x\ne 0$

Q. Which of the following is/are the zeros of the polynomial, $p\left(x\right)=x^2-5x+6$?

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

Q. X and Y are two towns. A man goes from town X to town Y at an average speed of $30$ km per hour and returns at an average speed of $20$ km per hour. Find the distance between the two towns if a man takes $10$ hours on the whole.

1. $110$ km
2. $50$ km
3. $40$ km
4. $120$ km

Q. Which of the following is/are the zeros of the polynomial, $p\left(x\right)=x^2-5x+6$?

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

Q. Solve the following equation:
$\sqrt{1+4x-x^2}=x-1$

Q. The zeroes of the polynomial $x^2-x-12$ are $3,4.$

1. True
2. False

Q. The roots of the quadratic equation $x^2-5x+6=0$ are .

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

Q. Solve
$-{\int }_{-4}^{-3}\sqrt{-\left(x+3\right)}dx$

Q. Find the rational roots of the polynomial $f\left(x\right)=2x^2+x^2-7x-6$.