The roots of q quadratic #x^2-sqrt(20x)+2=0# are c and d. Without using calculator show that #1/c+1/d=sqrt(5)#?

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#1/c+1/d=sqrt(5)#

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Answer 1 · 2018-01-22T09:43:08

See the proof below

If the roots of a quadratic equation #ax^2+bx+c=0# are

#alpha # and #beta# then,

#alpha+beta=-b/a#

and

#alpha beta=c/a#

Here the quadratic equation is #x^2-sqrt20 x+2=0#

and the roots are #c# and #d#

Therefore,

#c+d=sqrt20#

#cd=2#

so,

#1/c+1/d=(d+c)/(cd)#

#=(sqrt20)/2#

#=(2sqrt5)/2#

#=sqrt5#

#QED#