Question

Solve the Equation 3x3–x+88=4x23x^{3} – x + 88 = 4x^{2}3x3–x+88=4x2 if one of the root of the given cubic polynomial equation is 2 − 7 i\mathbf{2\;-\;\sqrt{7}\;i}2−7i.

Answer 1

Explanation:

Quadratic equations 3x

2

+ax+1=0 and 2x

2

+bx+1=0 have a common root.

Let α be the common root.

⇒3α

2

+aα+1=0…(1)

and 2α

2

+bα+1=0…(2)

Multiplying (1) by 2 and (2) by 3.

Further solving those two equations for α gives

α=b−a…(3)

Substituting (3) in(1)

⇒2(b−a)

2

+b(b−a)+1=0

⇒3b

2

+2a

2

−5ab+1=0

∴5ab−3b

2

−2a

2

=1