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For some real number $r,$ the polynomial $8x^3 - 4x^2 - 42x + 45$ is divisible by $(x - r)^2.$ Find $r.$

 

My go at it:

I immediately tried factoring it, and magically, the factored expression was:

 

$(2x-3)^2(2x+5)$, obviously we want (x-r)^2 to be divisible so I though 3x+3 would divide the $(2x-3)^2$, 

 

however the question is asking for a real number $r$, then is there a number $r3?, 

Remember, vietas formula for three roots is for x, y, z are roots,

 

x+y+z=-b/a

xy+yz+xz=c/a

xyz=-d/a 

 

for a cubic polynomial ax^3+bx^2+cx+d

 Jan 1, 2021
 #1
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Sorry there is a typo, for r3, it is $r$

 Jan 1, 2021
 #2
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Hints?

 Jan 1, 2021
 #3
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Hi even if you dk what to do can you guys try to give it a try so I could get an idea. Sorry if I sound impatient.

 Jan 1, 2021
 #4
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$:($

.
 Jan 1, 2021

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