Problem 1 :
If the sides of a cubic box are increased by 1, 2, 3 units respectively to form a cuboid then the volume is increased by 52 cubic units. Find the volume of the cuboid.
Problem 2 :
Construct a cubic equations with roots
i) 1, 2 and 3
ii) 1, 1 and -2
iii) 2, 1/2 and 1
Problem 3 :
If α, β and γ are the roots of the cubic equation
x^{3} + 2x^{2} + 3x + 4 = 0
form a cubic equation whose roots are
i) 2α, 2β and 2γ
ii) 1/α, 1/β and 1/γ
iii) -α, -β and -γ
Problem 4 :
Solve the equation
3x^{3} - 16x^{2} + 23x - 6 =0
if the product of two roots is 1.
Problem 5 :
Find the sum of the square of roots of the equation
2x^{4} - 8x^{3} + 6x^{2} - 3 = 0
Problem 6 :
Solve the equation
x^{3} - 9x^{2} + 14x + 24 = 0
if it is given that two of its roots are in the ratio 3 : 2.
Problem 7 :
If α, β and γ are the roots of the polynomial equation
ax^{3} + bx^{2} + cx + d = 0
find the value of Σα/βγ in terms of the coefficients.
Problem 8 :
If α, β, γ and δ are the roots of the polynomial equation
2x^{4} + 5x^{3} - 7x^{2} + 8 = 0
find a quadratic equation with integer coefficients whose roots are α + β + γ + δ and α β γ δ.
Problem 9 :
If p and q are the roots of equation lx^{2} + nx + n = 0, show that √(p/q) + √(q/p) + √(n/l) = 0
Problem 10 :
If the equations x^{2} + px + q = 0 and x^{2} + p'x + q' = 0 have a common root, show that it must be equal to
Problem 11 :
A 12 meter tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was left standing.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM