state the value of the discriminant and the discribe the nature of the solution 20x^2-8x-17=0

Answer 1

The discriminant is
b^2 -4ac = 8^2 - 4*(-17)*20
= 64 + 1360 = 1424

The fact that is is positive and not zero implies the equation has two real solutions. They are both irrational, since 1424 is not a perfect square.