Hey Everyone!
I was wondering if any here could answer these two questions.
I thought people may find it interesting to try and solve these two questions.
Who can solve it first?
Question 1:
The cubic equation ax^3+bx^2+cx+d=0 has the property that two roots are the reciprocals of each other. Prove that a^2 - d^2 = ac - bd .
Verify that this condition holds for the equation 9x^3 + 24x^2 - 11x -6 = 0, and solve it .
Question 2:
The roots of the equation x^3+ax+b=0 are α, β and γ.
Find the equation with the roots β/γ + γ/β , γ/α + α/γ and α/β + β/α
I was wondering if any here could answer these two questions.
I thought people may find it interesting to try and solve these two questions.
Who can solve it first?
Question 1:
The cubic equation ax^3+bx^2+cx+d=0 has the property that two roots are the reciprocals of each other. Prove that a^2 - d^2 = ac - bd .
Verify that this condition holds for the equation 9x^3 + 24x^2 - 11x -6 = 0, and solve it .
Question 2:
The roots of the equation x^3+ax+b=0 are α, β and γ.
Find the equation with the roots β/γ + γ/β , γ/α + α/γ and α/β + β/α