Given the Trinomial 5x^2- 2x-3, predict the type of solutions

Answer: Two distinct real roots.Step-by-step explanation: Given a quadratic equation [tex]ax^2+bx+c=0[/tex], we can predict the type of solution by calculating the Discriminant (D): [tex]D=b^2-4ac[/tex] Identify a, b and c from [tex]5x^2- 2x-3=0[/tex]. [tex]a=5\\b=-2\\c=-3[/tex] Substitute into the formula of the Discriminant. Then: [tex]D=(-2)^2-4(5)(-3)\\D=64[/tex] The discriminant obtained is greater than zero. When [tex]D>0[/tex] the type of solution is: two distinct real roots.