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The solutions to

2x^2 - 10x + 13 = x^2 - 17

are a + bi  and a  - bi where a and b are positive. What is ab?

 Jun 30, 2022
 #1
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+1

$\displaystyle \sqrt{125} \ or \ 5\sqrt{5}$ 

 

now can you help me with my question?

 Jun 30, 2022
 #2
avatar+124676 
+1

Rearrange as

 

x^2 - 10x + 30 =  0

 

Sum of the roots =   10 / 1  =  10       so a =  5

 

Product of the  roots =  30

 

(5 + bi) ( 5 - bi) =   30

 

25 + b^2  = 30

 

b^2  =  30  - 25

 

b^2 =  5

 

b = sqrt (5)

 

ab = 5sqrt (5)

 

 

cool cool cool

 Jun 30, 2022

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