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If a is a root of 4x²+2x-1=0, then the other root is 1)3a³-4a 2) 4a³-3a 3) 3a³+4a 4) 4a³+3a


If a is a root of 4x²+2x-1=0, then the other root is


1)3a³-4a                          2) 4a³-3a                            3) 3a³+4a


4) 4a³+3a


Grade:10

2 Answers

Menka Malguri
39 Points
9 years ago

Let the other root be b.

According to the quadratic equation theory,

sum of roots=-(B/A)

so,a+b=-2/4=-1/2

b=-1/2a

I suggest you to check your question and post it again.

Hope that works.

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Sudhanshu,

 

Note that the roots of this equation are {root(5)-1}/4 ------- which is cos72

and -{root(5)+1}/4 -----------which is -cos36.

 

Now -cos36 = cos(36+180) = cos(216) = cos(3*72)

Now cos3x = 4cos^3 x - 3cosx....

So if one root is "a" (=cos72), then the other root is 4a^3-3a..... and that would be option (2).

 

Best Regards,

Ashwin (IIT Madras).

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