Problem 1 :
Find the sum and product of the roots of :
3x^{2} – 2x + 7 = 0
Problem 2 :
Find the sum and product of the roots of :
x^{2} + 11x - 13 = 0
Problem 3 :
Find the sum and product of the roots of :
5x^{2} – 6x - 14 = 0
Problem 4 :
The equation kx^{2} – (1 + k)x + (3k + 2) = 0 is such that the sum of its roots is twice their product. Find k and the two roots. Solution
Problem 5 :
The quadratic equation ax^{2} – 6x + a - 2 = 0, a ≠ 0, has one root which is double the other.
a) Let the roots be α and 2α. Hence find two equations involving α.
b) Find α and the two roots of the quadratic equation.
Problem 6 :
The quadratic equation kx^{2} + (k–8)x + (1 – k) = 0, k ≠ 0, has one root which is two more than the other. Find k and the two roots. Solution
Problem 7 :
The roots of the equation x^{2} – 6x + 7 = 0 are α and β. Find the simplest quadratic equation with roots
α + 1/β and β + 1/α.
Problem 8 :
The roots of 2x^{2} – 3x - 5 = 0 are p and q. Find all quadratic equations with roots p^{2} + q and q^{2} + p.
Problem 9 :
kx^{2 }+ (k + 2) x - 3 = 0
has roots which are real and positive. Find the possible values that k may have.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM