# The quadratic equation # x^2+px+q = 0# has a complex root #2+3i#. Find #p# and #q#?

##### 2 Answers

# p=-4 #

# q=13 #

#### Explanation:

Suppose the roots of the general quadratic equation:

# ax^2+bx+c = 0 #

are

# "sum of roots" \ \ \ \ \ \= alpha+beta = -b/a #

# "product of roots" = alpha beta \ \ \ \ = c /a #

Complex roots always appear in conjugate pairs, so if one root of the given quadratic is

# x^2+px+q = 0#

we know that:

# alpha+beta = -p/1 \ \ \ # ; and# \ \ \ alpha beta = q/1 #

And we can calculate:

# alpha + beta = 2+3i + 2-3i = 4 => p=-4 #

# alpha beta = (2+3i)(2-3i) = 4+9 = 13 => q=13 #

#### Explanation:

It is known that **Quadr. Eqn.**

Therefore,

Comparing the **Real** and **Imaginary Parts** of both sides, we get,

**Respected Steve Sir,** has alreay derived.

**Enjoy Maths.!**