Find the values of R for which the equation have equal roots x²(R+2)x+R²=0?

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Answer 1 · 2018-01-09T10:35:53

#R=2,-2/3#

for any quadratic equation

#ax^2+bx+c=0#

it has equal roots if

#b^2-4ac=0#

we have

#x^2+(R+2)x+R^2=0#

equal roots

#=>(R+2)^2-4R^2=0#

#R^2+4R+4-4R^2=0#

factorising by grouping

#=>3R^2-4R-4=0#

#3R^2-6R+2R-4=0#

#3R(R-2)+2(R-2)=0#

#(3R+2)(R-2)=0#

#R-2=0=>R=2#

#3R+2=0=>R=-2/3#