Solving a Quadratic Equation by Completion of Squares Method

Q.

$150$ workers were engaged to finish a piece of work in a certain number of days. $4$ workers dropped the second day, $4$ more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is

1. $15$

2. $20$

3. $25$

4. $30$

Q.

Which of the following is a quadratic equation?

1. $x^2+2x+1={(4-x)}^2+3$

2. $-2x^2=(5-x)(2x-(\frac{2}{5}\left)\right)$

3. $(k+1)x^2+\left(\frac{3}{2}\right)x=7,wherek=-1$

4. $x^3-x^2={(x-1)}^3$

Q.

Solve the following:
Radha takes some flowers in a basket and visits three temples one-by-one. At each temple, she offers one half of the flowers from the basket. If she is left with $3$ flowers at the end, then find the number of flowers she had in the beginning.

Q.

Two candles of same height but different thickness are lighted. The first burns of in 6 hrs and the second in 8 hrs. How long after lighting the both will the first candle be half of the second ?

Q.

$3$ chairs and $2$ tables costs $Rs.700$ and $5$ chairs and $3$ tables costs $Rs.1100$. What is the cost of $2$ chairs and $2$ tables?

Q.

(i) One year ago, a man was 8 times as old. as his son. Now, his age is equal to the square of his son's age. Find their present ages.
(ii) A man is $3\frac{1}{2}$ times as old as his son. If the sum of the squares of their ages is 1325, find the ages of the father and the son.

Q.

Solve the following:

A lady went to a bank with Rs. 100000. She asked the cashier to give her Rs. 500 and Rs. 1000 currency notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes.

Q. Solve for x by completing the square method:
$x^2-(\sqrt{3}+1)x+\sqrt{3}=0$

1. 1 and $\sqrt{3}$
2. 2 and $\sqrt{3}$
3. 1 and 2
4. 3 and 4

Q.

Find $x$: $\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+}}}...\infty =6$

Q.

If $2-i$ is a root of the equation $a{x}^2+12x+b=0$(where $a$ and $b$ are real), then the value of $ab$is

1. $45$

2. $15$

3. $-15$

4. $-45$

5. $25$

Q.

If $y=\sqrt{\sqrt{7}+7+\sqrt{8+2\sqrt{7}}}-\sqrt{7}$, then the value of y will be:

1. 1

2. $\sqrt{7}$

3. $8-2\sqrt{7}$

4. $\sqrt{7}-1$

Q.

What is a quadratic equation? How can you solve a quadratic equation by factorization method?

Q.

The roots of the equation $(x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0a\in \mathrm{ℝ}$ are always

1. equal

2. imaginary

3. real and distinct

4. rational and equal

Q. The number that is to be added to $x^2+12x$ to make it a perfect square is .

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

Q.

If $f\left(x\right)={\cos }^{-1}\left(x-x^2\right)+\sqrt{1-\frac{1}{\left|x\right|}}+\frac{1}{\left[x^2-1\right]}$, then the domain of $f\left(x\right)$ is

1. $\left[-\sqrt{2},\frac{1-\sqrt{5}}{2}\right]$

2. $\left[\sqrt{2},\frac{1+\sqrt{5}}{2}\right]$

3. $(\sqrt{2},\frac{1+\sqrt{5}}{2}]$

4. None of these

Q.

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

Q.

The solution set of the equation ${\left(5+2\sqrt{6}\right)}^{x^2-3}+{\left(5-2\sqrt{6}\right)}^{x^2-3}=10$ is

1. $\left\{\pm 2,\pm \sqrt{2}\right\}$

2. $\left\{\pm 3,\pm \sqrt{3}\right\}$

3. $\left\{\pm 5,\pm \sqrt{5}\right\}$

4. $\left\{\pm 6,\pm \sqrt{6}\right\}$

Q. Places A and B are 160 km apart on a highway. One car starts from A and another car from B at the same time. If they travel in the same direction , they meet in 8 hours. But, if they travel towards each other, they meet in 2 hours. Find the speed of each car.

Q.

A motorboat whose speed is 9 km/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream.

Q.

The product of 2 consecutive natural numbers is 72. Find the numbers.

1. 8, 9

2. -8, -9

3. 36, 2

4. 18, 4

Q. Solve for x: $\sqrt{6x+7}-(2x-7)=0$

Q.

Question 18
Which of the following is not true?
(A) $(7+8)+9=7+(8+9)$
(B) $(7\times 8)\times 9=7\times (8\times 9)$
(C) $7+8\times 9=(7+8)\times (7+9)$
(D) $7\times (8+9)=(7\times 8)+(7\times 9)$

Q.

In a lucky draw, Rs 9, 000 were divided equally among a certain number of people. Had there been 20 more people, each would have got Rs 160 less. Find the original number of people.

1. 24

2. 25

3. 26

4. 27

Q.

Which constant must be added and subtracted to solve the quadratic equation $9x^2+\frac{3}{4}x-2=0$ by the method of completing the square?

1. $\frac{9}{64}$

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

3. $\frac{1}{8}$

4. $\frac{1}{64}$

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

1. $x=2\pm \sqrt{13}$
2. $x=4\pm \sqrt{5}$
3. $x=2\pm \sqrt{3}$
4. $x=2\pm \sqrt{6}$

Q.

Find the polynomial whose sum of zeroes is $-\frac{8}{5}$ and the products of zeroes is $\frac{7}{5}$.

1. 

2. 

3. 

4. 

Q.

The length of a rectangle is twice its breadth and its area is 288 $c{m}^2$. Find the dimensions of the rectangle.

Q.

The zero of the polynomial p(x) =5x - 10 is ________

___

Q.

The manufacturer of a certain item can sell all he can produce at the selling price of $\mathrm{Rs}.60$ each. It costs him $\mathrm{Rs}.40$ in materials and labour to produce each item and he has overhead expenses of $\mathrm{Rs}.3000$ per week in order to operate the plant. The number of units he should produce and sell in order to make a profit of at least $\mathrm{Rs}.1000$ per week is:

1. $200$

2. $250$

3. $300$

4. $400$

Q.

Check whether the following are quadratic equations: