Find a and b if x+2 is a factor of x square +ax+2b and a+b=4
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focus on (x+2) is a factor of x^2+ax+2b=0
So the (x+2) is satisfy this equation
put x+2 = 0 and get the value of x=-2
and put this value in the equation then,
(-2)^2+a(-2)+2b=0,(-2)(-2)+a(-2)+2b=0,4-2a+2b=0,-2(a-b)=-4,a-b=2 equation no 1and other give equation is a+b=4, equation no 2
so two equation , two variable you can find the value of a and b easily by substitution method.from equation 1a=2b2b+b=4b=4/3put the value of 'b' in the equation no 1a=2(4/3)a=8/3 value of a=8/3 and b= 4/3
Hence Proof.
focus on (x+2) is a factor of x^2+ax+2b=0
So the (x+2) is satisfy this equation
put x+2 = 0 and get the value of x=-2
and put this value in the equation then,
(-2)^2+a(-2)+2b=0,(-2)(-2)+a(-2)+2b=0,4-2a+2b=0,-2(a-b)=-4,a-b=2 equation no 1and other give equation is a+b=4, equation no 2
so two equation , two variable you can find the value of a and b easily by substitution method.from equation 1a=2b2b+b=4b=4/3put the value of 'b' in the equation no 1a=2(4/3)a=8/3 value of a=8/3 and b= 4/3
Hence Proof.
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