Determine the values of #a# and #b#?
The equations #x^3+x^2+ax+b=0# and #x^3-bx^2-ax+4=0# both have #x=2# as a solution
The equations
2 Answers
Explanation:
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Explanation:
#"since x = 2 is a solution to both equations we can"#
#"substitute this value directly into the equations"#
#rArr2^3+2^2+2a+b=0" and "#
#2^3-2^2b-2a+4=0#
#"simplifying to give"#
#8+4+2a+b=0rArr2a+b=-12to(1)#
#8-4b-2a+4=0rArr-2a-4b=-12to(2)#
#"adding equations "(1)" and "(2)" to eliminate a"#
#(2a-2a)+(b-4b)=-12+(-12)#
#rArr-3b=-24rArrb=8#
#"substitute this value in equation "(1)#
#2a+8=-12rArr2a=-20rArra=-10#
#rArra=-10" and "b=8#