IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>EVERYDAY MATHEMATICS>Q 15

HARD

10th Foundation

IMPORTANT

Earn 100

In the Maths Olympiad of $2020$ at Animal Planet, two representatives from the donkey’s side, while solving a quadratic equation, committed the following mistakes.
(i) One of them made a mistake in the constant term and got the
roots as $5$ and $9$ .
(ii) Another one committed an error in the coefficient of $x$ and he
got the roots as $12$ and $4$ .
But in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the quadratic equation.

60% studentsanswered this correctly

Important Questions on Quadratic Equations

EASY

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>EVERYDAY MATHEMATICS>Q 16

₹ 6500

were divided equally among a certain number of people. If there had been

15

more people, each would have got

₹ 30

less. Find the original number of people.

MEDIUM

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>EVERYDAY MATHEMATICS>Q 17

Swati can row her boat at a speed of

5

km/hr in still water. If it takes her

1

1 hour more to row the boat

5.25

km upstream than to return downstream, find the speed of the stream.

EASY

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>ACHIEVERS SECTION (HOTS)>Q 18

Which of the following equations has two distinct real roots?

EASY

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>ACHIEVERS SECTION (HOTS)>Q 19

Read the statement carefully and state ‘T’ for true and ‘F’ for false.
(i) The value of

2 + \frac{1}{2 + \frac{1}{2 + \dots \infty}}

is

\sqrt{2}

.
(ii) A line segment

AB

of length

2 m

is divided at

C

into two parts such that

{AC}^{2} = AB ∙ CB .

The length of the part

CB

is

3 + \sqrt{5}

.
(iii) Every quadratic equation can have at most two real roots.
(iv) A real number

α

is said to be the root of the quadratic equation

{ax}^{2} + bx + c = 0,

if

{aα}^{2} + bα + c = 0

.

MEDIUM

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>ACHIEVERS SECTION (HOTS)>Q 20

The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is

2 \frac{16}{21}

, find the fraction.