miscellaneous equation

miscellaneous equation

miscellaneous equations

miscellaneous equations NSEJS

NSEJS - exam paper

Singapore Maths Olympiad

If it is known that the roots of the equation are all integers, how many distinct roots does the equation have?

x⁵ + 3x⁴ – 4044118x³ – 12132362x² – 12132363x - 2011² = 0

Singapore maths Olympiad

miscellaneous example

Find the integral  roots of the equation:

x³  +8x² + 13x + 6 = 0

show  { √5 + 2}^1/3 - { √5 - 2}^1/3 = 1

Find the integral roots of the equation:

Find the integral  roots of the equation:

x³  - 10x² + 27x - 18 = 0

Find the roots of the equation:

Find the roots of the equation:

y⁴  - 2y³ - 21y² +22y + 40 = 0

Find the integral roots of the equation:

Find the integral  roots of the equation:

x⁴  + 4x³ + 8x + 32 = 0

Finding the Rational roots for the equation:

Find the Rational roots for the equation:

32 y³ - 6y - 1 = 0

Rational roots for the equation

Find the Rational roots for the equation:

6y³ -11y² + 6y - 1 = 0

finding rational roots of polynomial

Find the Rational roots for the equation:

96y³ -16y² -6y + 1 = 0

finding rational roots of polynomial

Find the Rational roots for the equation:

y⁴ – (40/3)y³ + (130/3)y² -40y + 9 = 0

finding rational roots

Find the Rational roots for the equation:

24y³ -2y² -5y + 1 = 0

miscellaneous equation

If α and β are the complex cube roots of unity, and x = a + b, y = aα+ bβ and z = aβ + bα, then the value of xyz =.............................

miscellaneous equations,

Solve for x:

3x² - 4√(3x² – 4x + 1) = 4x – 4 

miscellaneous equations

solve for x:

√x + √{x - √(1 – x)} = 1

miscellaneous equations

Find the real values of x, y and z for the equations
x + y = 2
xy - z²  = 1

IIT 72

miscellaneous equations

Solve for x, y and z

xy + x + y = 23
xz + z + x = 41
yz + y + z = 27

IIT