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The roots of $7x^2 + x - 5 = 0$ are $a$ and $b.$ Compute $(a - 4)(b - 4).$

 Jun 14, 2022
 #1
avatar+580 
+1

Using the quadratic formula gives:

 

1,2=1±1247(5)27

 

x1=1+14127,x2=114127

 

x=1+14114,x=114114

So if a and b are roots:

 

(1+141144)(1141144)

 

(EDIT:  Just you are calc if you don't know how to solve!!!)

 

Just solve that and you got the answer cool

 

-Vinculum

 Jun 14, 2022
edited by Vinculum  Jun 14, 2022
 #2
avatar
-1

by using vieta's formula, the answer is 80/7

 Jun 14, 2022
 #3
avatar+2668 
0

Expand: (a4)(b4)=ab4a4b+16=ab4(a+b)+16

 

By Vieta's formula, we know that ab=57 and a+b=17

 

Now, plugging this in, we get: 574(17)+16=57+47+16=1567

 Jun 14, 2022
 #4
avatar+580 
+1

I completely forgot bout the Vieta's formula

 

I knew I did something wrong when I got those crazy numbers

 

 

Thanks, BuilderBoi laugh

 Jun 15, 2022
 #5
avatar+349 
+1

Why did you like your comment when you got it wrong?

hipie  Jun 16, 2022
 #6
avatar+580 
0

I did?

 Jun 16, 2022

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