## Algebra 1

Sometimes true. Two equations are $10x^2+5x+1=0$ and $2x^2+4x+2=0$
One example of an equation without two solutions is $2x^2+4x+2=0$ The determinant is as follows: $b^2-4ac$ $4^2-4*2*2$ $16-8*2$ $16-16$ $0$ Since this determinant is zero, there is exactly one real solution for the equation. Another equation without two solutions is $10x^2+5x+1=0$ The determinant is as follows: $b^2-4ac$ $5^2-4*10*1$ $25-40$ $-15$ Since this determinant is less than zero, there are no real solutions for the equation.