Question; If alpha and beta are zeroes of P(X)=2X*2X - X - 6, find value of alpha -1 and beta -1? ThankYou

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Answer 1 · 2018-02-18T10:29:08

#alpha-1=1, beta-1=-4#

Given:

#alpha " is the root of "2x^2-x-6#

#beta " is the root of "2x^2-x-6#

#alpha-1=?, beta-1=?#

#"The roots are given by"#

#a=2, b=-1, c=-6#

#x=(-b+-sqrt(b^2-4ac))/(2a)#

#"Substituting"#

#x=(-(-1)+-sqrt((-1)^2-4xx2xx-6))/(2xx2)#

#x=(1+-sqrt(1+48))/4#

#x=(1+-sqrt49)/4=(1+-7)/4#

#"Thus,"#

#"Let"alpha=(1+7)/4=8/4=2#

#"Let"beta=(1-7)/4=-6/4=-3#

#"Now,"alpha-1=2-1=1, and beta-1=-3-1=-4#

#alpha-1=1, beta-1=-4#