Question

If (2+i) is one root form an equation

Answer 1

Answer:

The roots of x  

2

+px+q=0 are

[2+i  

3

​

] and [2−i  

3

​

]

Now, for x  

2

+px+q=0;

Sum of roots =−p

⇒ [2+i  

(

​

3)]+[2−i  

(

​

3)] =−p

⇒ 4=−p

⇒ p=−4

Similarly,

Product of roots =q

⇒ [2+i  

(

​

3)]×[2−i  

(

​

3)]=q

⇒ (2)  

2

−(i  

(

​

3))  

2

=q   using ((a+b)(a−b)=a  

2

−b  

2

)

⇒ 4−i  

2

.3=q

⇒ 4−(3)=q

⇒ q=7

So, p=−4 and q=7

Ordered pair is (−4,7)

p+q=−4+7=3

Step-by-step explanation:

hope it helps