Question 759771: If the equations x^2+2x-3=0 & x^2+3x-k=0 have a comman root then the non-zero value of k is: Answer by sachi(548) (Show Source):
You can put this solution on YOUR website! If the equations x^2+2x-3=0 & x^2+3x-k=0 have a comman root then the non-zero value of k is:
let us solve the eqn
x^2+2x-3=0
or x^2+3x-x-3=0
or x(x+3)-1(x+3)=0
or (x+3)(x-1)=0
x= -3 Or 1
now the 2nd eqn
x^2+3x-k=0
the roots x={-3+/-sqrt[3^2-4*1*-k]}/2=-3 Or 1
or ={-3+/-sqrt[3^2-4*1*-k]}=-6 or 2 multiplying 2 on RHS
or +/-sqrt[3^2-4*1*-k]}=-3 or 5 adding 3 on RHS
or 3^2-4*1*-k=9 or 25 squaring both sides
or 9+4k=9 or 25 simplifying
or 4k=0 or 16 subtracting 9 on RHS
or k=0 or 4 dividing 4
