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(2+3i)x^2 - bx + (3-i) = 0 , if one root is (2-i) then find out the another root and the value of b

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Maths

Complex Numbers and Quadratic Equations

The modulus and the Conjugate of a Complex number

If 2 + 3i is one of the roo...

MATHS

If 2+3i is one of the roots of the equation 2x

3

−9x

2

+kx−13=0,k∈R, then the real root of this equation :

MEDIUM

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ANSWER

Given equation is

2x

3

−9x

2

+kx−13=0 where k∈R

Since, any odd degree equation with real coefficients has at least one real root.

So, real root exist.

Let α be the real root.

Since, 2+3i is a root of the equation. So, other root will be 2-3i. (Imaginary roots always occurs in conjugate pairs.)

Now, sum of roots 2+3i+2−3i+α=

2

9

⇒α=

2

1