Solving a Quadratic Equation by Completing the Square

Q. What term should be added to $a^2+2ab$ to make it a perfect square?

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

Q. Find the roots of the equation $x^2–14x+17=0$ by the method of completing the square.

1. $x=7\pm \sqrt{52}$
2. $x=11\pm \sqrt{32}$
3. $x=7\pm \sqrt{32}$
4. $x=10\pm \sqrt{32}$

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

3. 7, $(x-\frac{1}{2}{)}^2-\frac{225}{4}$ = 0

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

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

1. $x=9\pm \sqrt{69}$
2. $x=9\pm \sqrt{67}$
3. $x=8\pm \sqrt{69}$
4. $x=6\pm \sqrt{69}$

Q.

Using the method of completion of squares find one of the roots of the equation $2x^2-7x+3=0$. Also, find the equation obtained after completion of the square.

1. 13, $(x-\frac{7}{2}{)}^2-\frac{25}{16}=0$

2. 3, $(x-\frac{7}{4}{)}^2-\frac{25}{16}=0$

3. 6, $(x-\frac{7}{4}{)}^2-\frac{25}{16}=0$

4. 3, $(x-\frac{7}{2}{)}^2-\frac{25}{16}=0$

Q. Find the roots of the equation $x^2–4x-9=0$ by the method of completing the square.

1. $x=2\pm \sqrt{-3}$
2. $x=4\pm \sqrt{-5}$
3. $x=2\pm \sqrt{-6}$
4. $x=2\pm \sqrt{-5}$

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. $\text{Which of the following operations can}$
$\text{convert the expression}(x^2+\frac{8x}{\sqrt{3}})$
$\text{into a perfect square?}$

1. $\text{Addition of}{\left(\frac{8}{\sqrt{3}}\right)}^2.$
2. $\text{Addition of}{\left(\frac{4}{\sqrt{3}}\right)}^2.$
3. $\text{Addition of}{\left(\frac{8}{3}x\right)}^2.$
4. $\text{Subtraction of}\frac{8x}{\sqrt{3}}$

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

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