if 3+4i is a root of equation x(square)+px+q=0 p,q belongs to rational number rhen p,q=?
Answers
Answer:
p=6,q=25
Step-by-step explanation:
alpha- 3+4i
beta- 3-4i
=> sum of roots- (-p/1)______¹
product of roots- q/1_____²
• so p=6
q=25
Given:
x² + px + q = o
with one root 3 + 4!
To Find:
Value of p and q
Solution:
We have given quadratic eqn
x² + px + q = o
whose one root is ( 3 + 4! )
as we know that if one root of quadratic eqn is complex no. then another root will be conjugate of it so, the other root will be ( 3 - 4! ).
So, the roots of eqn are 3 + 4! and 3 - 4!
The sum of the root of quadratic eqn is given by ( - P )
The product of the root of quadratic eqn is given by ( q )
Therefore,
3 + 4! + 3 - 4! = - p ( 3 + 4! ) × ( 3 - 4! ) = q
6 = -p 3² - (4!)² = q
p = -6 9 - ( - 16 ) = q
9 + 16 = q
25 = q
Hence, the value of p = -6 and q = 25.