exam Maths Puzzle Numerical Ability

Use the determinant to determine whether the quadratic equation has two unequal real solutions, a double real solution or no real solution without solving the equation: x^2-2x+2=0

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Can any give me a hand with this one? Thanks

Use the discriminant to determine the nature of the rools of each equation. DO NOT SOLVE THE EQUATION.

10x^2 + x = 21

Remember it says not to solve the equation. Thanks!
I am really confused with this homework problem.

I have two triangles that are congruent. The first triangle's measures are the sides of AB=13, AC=x(unknown), and the base BC=