Completing the Square

Q.

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

Q. What must be added to $x^2+2x$ to make it a perfect square?

1. $\frac{1}{2}$
2. 1
3. 0
4. 2

Q.

___ should be added to ${9x}^2+18x$ to make it a perfect square.

1. 9

2. 4

3. -9

4. 7

Q.

Find the roots of the following quadratic equation by the method of completing the square.
$4x^2+4\sqrt{3}x+3=0$

1. $-\frac{\sqrt{3}}{2}and-\frac{\sqrt{3}}{2}$

2. $-\frac{\sqrt{5}}{2}and-\frac{\sqrt{5}}{2}$

3. $-\frac{1}{\sqrt{3}}and-\frac{1}{\sqrt{3}}$

4. $-\frac{2}{\sqrt{3}}and-\frac{2}{\sqrt{3}}$

Q. Find the roots of the equation $x^2–18x+12=0$ by the method of completing the square.

1. $x=9\pm \sqrt{6}$
2. $x=6\pm \sqrt{62}$
3. $x=6\pm \sqrt{69}$
4. $x=9\pm \sqrt{69}$

Q. What number should be added to $x^2+12x$ so that the resultant is a perfect square?

1. 144
2. 36
3. 18
4. 72

Q.

Question 2 (ii)
Simplify $(3+\sqrt{3})(3-\sqrt{3})$ .

Q. How to find square root of polynomials?

Q.

Which one is in the simplest form for √112?

1. 5√7

2. 8√7

3. 4√7

4. 6√7

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

1. $\frac{3-\sqrt{19}}{5}$
2. $\frac{5+\sqrt{19}}{5}$
3. $\frac{3+\sqrt{19}}{5}$
4. $\frac{5-\sqrt{19}}{5}$

Q. Determine the square root of $x^4-6x^3+19x^3-30x+25$

1. $x^2-1$
2. $x^2-2x+42$
3. $x^2-3x+5$
4. $5-3x+21x^2$

Q.

Find one of the roots of the quadratic equation ${2x}^2-7x+3=0$ by the method of completion of the square. Also, what is the equation obtained after completion of the square?

1. 3

2. 12

3. 6

4. 13

Q.

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

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

2. $x=\frac{3\pm \sqrt{19}}{5}$​
   

3. $x=5$

4. $x=3$

Q. The roots of the quadratic equation $2x^2+5x-3=0$ are -3 and .

1. $\frac{1}{2}$
2. 3
3. 6

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

1. 6
2. 4
3. 9
4. 36

Q.

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

1. 36

2. 9

3. 72

4. 18

Q.

Solve the quadratic equation $4x^2+12x+9=81$ by completion of squares method.

1. x = 6, -3

2. x = 3, -6

3. x = 2, -4

4. x = 3, 3

Q. Find the roots of the following quadratic equation, by the method of completing the square:
$2x^2-7x+3=0$

Q. Find the roots of the following quadratic equation, by the method of completing the square:
$2x^2-7x+3=0$

Q. If ${(x+y)}^2=144$ and $x^2-y^2=24$, then what is $x$ if $x$ and $y$ are both positive?

1. $8$
2. $5$
3. $7$
4. $12$
5. $2$

Q.

What is the square root of $(4x^2–361)(4x^2+12x+9)(64x^2–5776)$ ?

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.

The square of (2$x$ -1) is equal to 5. If one of the values of $x$ is $\frac{1-\sqrt{5}}{2}$, what is the value of $x$ ?

1. x = (-1 - √5)/2

2. x= (1 + √5)/2

3. x = (-1 + √5)/2

4. x= (1 + √6)/2

Q. Find the roots of the following quadratic equation, by the method of completing the square:
$2x^2+x-4=0$

Q. Which of the following operations could help convert the expression $x^2+\frac{4x}{\sqrt{3}}$ a perfect square?

1. By adding $\left(\frac{4}{3}\right)$
2. By adding ${\left(\frac{8}{3}\right)}^2$
3. By adding $\left(\frac{4}{3}x\right)$
4. By adding $\left(\frac{8}{3}x\right)$

Q.

Find the square root of $\left[\right(x^2+5x+6\left)\right(x^2+7x+10\left)\right(x^2+8x+15\left)\right]$

Q. Using the method of completing the square, find the roots of $4m^2+4\surd 3m+3=0$.

1. $+\frac{\sqrt{3}}{2},-\frac{\sqrt{3}}{2}$
2. $-\frac{\sqrt{3}}{2},-\frac{\sqrt{3}}{2}$
3. $(\frac{3}{2}-\sqrt{3}),(-\frac{3}{2}-\sqrt{3})$
4. $-\frac{3}{2},-\frac{\sqrt{3}}{2}$

Q.

The product of 2 consecutive natural numbers is 56. Solve this problem using completing the square method of quadratic equation. Write the equation obtained after completing the square and also write the smaller of the 2 numbers.

1. 7, $(x+\frac{1}{2}{)}^2-\frac{225}{4}=0$

2. 7, $(x-\frac{1}{2}{)}^2-\frac{225}{4}$ = 0

3. 8, $(x+\frac{1}{2}{)}^2–\frac{225}{4}=0$

4. 8, $(x-\frac{1}{2}{)}^2-\frac{225}{4}=0$

Q. Question 1 (ii)
Find the roots of the following quadratic equations, if they exist, by the method of completing the square:
(ii) $2x^2+x-4=0$

Q. Find the roots of the following quadratic equation, by the method of completing the square:
$2x^2+x-4=0$