Question #041c7

2 Answers
Jim G.
Feb 13, 2018

#x=-1/4" or "x=-1/2#

Explanation:

#"factorise the quadratic using the a-c method"#

#"the factors of + 8 which sum to + 6 are + 2 and + 4"#

#rArr8x^2+6x+1=0#

#rArr(4x+1)(2x+1)=0#

#"equate each factor to zero and solve for x"#

#4x+1=0rArrx=-1/4#

#2x+1=0rArrx=-1/2#

Jeremiah W.
Feb 13, 2018

The answers to #8x^2+6x+1=0# are #-1/4# and #-1/2#

Explanation:

Because this equation is a polynomial, meaning that we have an #x^2#, and the expression is equal to zero we know that we need to use the quadratic formula:

#(-b+-sqrt(b^2-4*a*c))/(2*a)#

where

#a=8#
#b=6#
#c=1#

Now we can just plug in each value into the formula to find our values.

NOTE:
There will be two values because we have a #+-#. This just means that at a certain point in the process we will have to

#-b+sqrt(b^2-4*a*c)#

AND

#-b-sqrt(b^2-4*a*c)#

The process would look like this:

#(-6+-sqrt(6^2-4*8*1))/(2*8)#

#(-6+-sqrt(6^2-4*8*1))/(2*8)#

#(-6+-sqrt(4))/(16)#

#(-6+-2)/(16)#

At this point would separate the #+-# into + and -

#(-6+2)/(16)#, #(-6-2)/(16)#

#-4/16#, #-8/16#

After simplifying, this gives us two answers:

#-1/4#, and #-1/2#

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