Solving by Completion of squares method

Q.

The cubic equation, whose roots are thrice to each of the roots of $x^3+2x^2-4x+1=0$ is

1. $x^3-6x^2+36x+27=0$

2. $x^3+6x^2+36x-27=0$

3. $x^3+6x^2+36x+27=0$

4. $x^3+6x^2-36x+27=0$

Q.

Find the roots of the equation $5x^2–6x–2=0$ by the method of completing the square.

1. $\frac{5\pm \sqrt{19}}{3}$

2. $\frac{3\pm \sqrt{19}}{5}$​

3. $5$

4. $3$

Q.

Solve the following quadratic equation by completing the squares :

$x^2-x-6=0$.

Q.

Find the roots of the equation $5x^2–6x–2=0$ by completing the square method.

1. $3$

2. $5$

3. $\frac{3\pm \sqrt{19}}{5}$​

4. $\frac{5\pm \sqrt{19}}{3}$

Q.

What number should be added to ${9x}^2$ + 18 $x$ to make it a perfect square?

Q. Match the expressions on the left with the number to be added to it to make the resultant a perfect square.

1. 81
2. 4
3. 121

Q.

A motor boat has a speed of 18 $\frac{km}{hr}$ in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream in $km/hr.$

1. $4km/hr$

2. $5km/hr$

3. $6km/hr$

4. $7km/hr$

Q. must be added to $a^2+2ab$ to make it a perfect square.

1. $b$
2. $a^2$
3. $2ab$
4. $b^2$

Q. One of the roots of the equation $(x+\frac{1}{a}{)}^2-b^2=0$ is .

1. $-ba$
2. $-a+b$
3. $-b-\frac{1}{a}$
4. $b+\frac{1}{a}$

Q. The number that is to be added to $x^2+6x$ to make the resultant a perfect square is .

1. 36
2. 18
3. 9
4. 72

Q. There are three figures of areas $x^2,12x$ and $z$ in the below figure. Figures A and C are squares while figure B is a rectangle, with length of one side as $x.$ What should be the value of $z$ so that all the 3 figures can be arranged to form a square of side (x +6)?

1. 16
2. 36
3. 18
4. 24

Q.

What number should be added to $x^2+6x$ to make it a perfect square?

1. 9

2. 72

3. 36

4. 18

Q.

Solve the quadratic equation 4$x^2$+ 5$x$ = 0 by completion of squares method. In the given options one of the options has one root and also the converted form of equation after completing the square. Select this option

1. x= 0, $({2x+\frac{5}{4})}^2$ - $\frac{5}{2}$ =0

2. $x$= $-\frac{5}{4}$, $({2x+\frac{5}{4})}^2$ - $\frac{5}{2}$ =0

3. $x$= $-\frac{5}{4}$, $({2x+\frac{5}{4})}^2$ -$({\frac{5}{4})}^2$=0

4. $x$= $-\frac{5}{2}$ , $(2x-5{)}^2$ - $({\frac{5}{4})}^2$=0

Q.

Solve the following quadratic equation by completing the squares :

$x^2-x-20=0$.