Question

Which of the following equation have only one solutions? Select all correct answers.

4x^2+4x=0
X^2+6x+9=0
9x^2-25=0
5x^2+20x+20=0
X^2-x-6=0

Answer 1

The equations which have only one solution are x²+6x+9=0 and 5x²+20x+20=0,

Explanation:

Answer 2

`4x^2+4x=0 \\ 4x(x+1)=0 \\ 4x=0 \ \lor \ x+1=0 \\ x=0 \ \lor \ x=-1 \\ \hbox{two solutions} \\ \\ x^2+6x+9=0 \\ (x+3)^2=0 \\ x+3=0 \\ x=-3 \\ \hbox{one solution}`


`9x^2-25=0 \\ (3x)^2-5^2=0 \\ (3x-5)(3x+5)=0 \\ 3x-5=0 \ \lor \ 3x+5=0 \\ 3x=5 \ \lor \ 3x=-5 \\ x=(5)/(3) \ \lor \ x=-(5)/(3) \\ \hbox{two solutions} \\ \\ 5x^2+20x+20=0 \\ x^2+4x+4=0 \\ (x+2)^2=0 \\ x+2=0 \\ x=-2 \\ \hbox{one solution}`


`x^2-x-6=0 \\ x^2+2x-3x-6=0 \\ x(x+2)-3(x+2)=0 \\ (x-3)(x+2)=0 \\ x-3=0 \ \lor \ x+2=0 \\ x=3 \ \lor \ x=-2 \\ \hbox{two solutions}`

The equations which have only one solution are: x²+6x+9=0 and 5x²+20x+20=0,