Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.3>Q 36

HARD

IOQM - PRMO and RMO

IMPORTANT

Earn 100

Find the value of the smallest positive integer $m$ such that the equation $x^{2} + 2 (m + 5) x + (100 m + 9) = 0$ has only integer solutions.

50% studentsanswered this correctly

Important Questions on Algebra

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.3>Q 37

Given that

(m - 2)

is a positive integer and it is also a factor of

3 m^{2} - 3 m + 10

. Find the sum of all such values of

m .

EASY

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.3>Q 38

Let

a

and

b

be the roots of the equation

x^{2} - m x + 2 = 0

. Suppose that

(a + \frac{1}{b})

and

(b + \frac{1}{a})

are the roots of the equation

x^{2} - p x + q = 0 .

What is

2 q

?

EASY

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.3>Q 39

The quadratic equation

x^{2} + m x + n = 0

has roots that are twice those of

x^{2} + p x + m = 0

, and none of

m, n

and

p

is zero. What is the value of

\frac{n}{p}

?

EASY

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.3>Q 40

What is the negative of the sum of the reciprocals of the roots of the equation

\frac{2003}{2004} x + 1 + \frac{1}{x} = 0 ?

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.3>Q 41

Both roots of the quadratic equation

x^{2} - 63 x + k = 0

are prime numbers. The number of possible values of

k

is

EASY

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.3>Q 43

Let

a, b,

and

c

be real numbers such that

a - 7 b + 8 c = 4

and

8 a + 4 b - c = 7 .

Then

a^{2} - b^{2} + c^{2}

is

HARD

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.3>Q 44

The zeros of the function

f (x) = x^{2} - a x + 2 a

are integers. What is the sum of all possible values of

a

?

EASY

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.4>Q 2

Given that

- 2

is the solution of the equation

\frac{1}{3} m x = 5 x + {(- 2)}^{2},

find the value of the expression

|{(m^{2} - 11 m + 17)}^{2007}|