Formation of Quadratic Equation from Roots

Q.

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. Find out the number of toys produced on that day.

1. 24

2. 25

3. 29

4. 30

Q. The roots of the quadratic equation $x^2-9x+14=0$ are

1. -7, -2
2. 7, 2
3. -7, 2
4. 7, -2

Q.

A train travels a distance of $480km$ at a uniform speed. If the speed had been $8km/h$ less, then it would have taken $3$ hours more to cover the same distance. Find the speed of the train.

1. 60 kmph

2. 50 kmph

3. 40 kmph

4. 10 kmph

Q.

Find the quadratic equation whose solution set is (2, -3)

1. (x + a) (x – 2a)

2. (x – 2a) (x + 2a)

3. (x + a) (x + 2a)

4. (x – a) (x – a)

Q. Question 2(ii)
(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. Find out the number of toys produced on that day.

Q. A mixture of 70 litres of wine and water contains $10\%$ water. How much water must be added to make the water content $12.5\%$ of the resulting mixture?

1. 1 litre
2. 2 litre
3. 3 litre
4. 4 litre

Q.

Frame the quadratic equation whose roots are -5, -12

1. $x^2+17x-60=0$

2. $x^2-17x+60=0$

3. $x^2+17x+60=0$

4. $x^2-17x-60=0$

Q.

If one of the roots of a quadratic equation is 5 and the product of their roots is -165, then the quadratic equation is :

1. $x^2+28x+165=0$

2. $x^2-28x+165=0$

3. $x^2+28x-165=0$

4. $x^2-28x-165=0$

Q. Roots of quadratic equation $2x^2-5x-3=0$ are

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

Q.

1. Speed of rowing in still water: 10 km/hr and the speed of the current: 5 km/hr.
2. Speed of rowing in still water: 8 km/hr and the speed of the current: 7 km/hr.
3. Speed of rowing in still water: 6 km/hr and the speed of the current: 4 km/hr.
4. Speed of rowing in still water: 18 km/hr and the speed of the current: 12 km/hr.

Q. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages was 48 years. Frame the equation for the above situation and predict the nature of its roots.

Q. Find the roots of $3x^2-10x+8=0$

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

Q. If one root of quadratic equation $x^2+3x-P=0$ is $2$, find the value of $P$.

Q.

A mixture of 70 litres of wine and water contains $10\%$ of water. What quantity of water must be added to make the water content $12.5\%$ of the resulting mixture?

1. 2 litre

2. 3 litre

3. 4 litre

4. 1 litre

Q. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ₹ 90, find the number of articles produced and the cost of each article.

Q.

The quadratic equation which has D = 0 and a root as $\frac{1}{10}$ is

1. $x^2-20x-100=0$

2. $x^2-100x-100=0$

3. $100x^2-20x+100=0$

4. $100x^2-20x+1=0$

Q. A train travels a distance of $480km$ at a uniform speed. If the speed had been $8km/h$ less, then it would have taken $3$ hours more to cover the same distance. We need to find the speed of the train.

Q. Represent the following situations in the form of quadratic equations :
(i) The area of a rectangular plot is $528m^2$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Q. A train travels a distance of $480km$ at a uniform speed. If the speed had been $8km/h$ less, then it would have taken $3$ hours more to cover the same distance. We need to find the speed of the train.

Q. A motor boat can travel $30$ km upstream and $28$ km downstream in $7$ hours , it can travel $21$ km upstream and return in $5hours$ find the speed of the boat in still water and the speed of the stream.

Q.

The sum of the ages of two friends is 20 years. Four years ago, the product of their ages was 48 years. Frame the equation for the above situation and predict the nature of its roots.

1. $x^2+20x+112=0$

   The roots are real and negative

2. $x^2-20x-112=0$

   The roots are real and positive

3. $x^2-20x+112=0$

   No real roots

4. $x^2+20x-112=0$

   The roots are real and equal

Q. Form the quadratic equation whose roots are:

1. $x^2+4x-45=0$
2. $x^2-14x-45=0$
3. $x^2+14x-45=0$
4. $x^2-4x-45=0$

Q. A number consists of two digits whose sum is $9$. If $9$ subtracted from the number, the digits interchange their places. Find the number.

Q. A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs. 1 less. How many books did he buy?
[3 Marks]

Q. Roots of quadratic equation $x^2-x-132=0$ are

1. $-12,11$
2. $-12,-11$
3. $12,-11$
4. $12,11$

Q. If one of the zeroes of a quadratic polynomial of the form $x^2+ax+b$ is the negative of the other, then it

1. has no linear term and the constant term is positive.
2. has no linear term and the constant term is negative.
3. can have a linear term but the constant term is negative.
4. can have a linear term but the constant term is positive.

Q. Choose the best possible option.
$(x+5)(x-8)=0$ is quadratic equation.

1. Yes
2. No
3. Complex equation
4. None

Q. If $\alpha$ and $\beta$ are the roots of the equation $a{x}^2+bx+c=0$. Find the equation whose roots are as given below.
$\frac{1}{\alpha +\beta },\frac{1}{\alpha }+\frac{1}{\beta }$

Q. Consider the following linear programming problem:

Maximize	$5X+6Y$
Subject to:	$4X+2Y\le 420$
	$1X+2Y\le 120$
	all variables $\ge 0$

Which of the following points $(X,Y)$ is feasible?

1. $(50,40)$
2. $(30,50)$
3. None of these
4. $(60,30)$
5. $(90,20)$

Q. A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. Find out the number of toys produced on that day.
[2 Marks]