Determine the discriminate of the quadric equation below Use

Determine the discriminate of the quadric equation below. Use the value of the discriminate to determine whether the quadric equation has two rational solutions, two irrational solutions, one repeated real solution, or two complex solutions that are not real. 2x = 5x^2 - 1 The value of the discriminate is. Choose the nature of the solution. One repeated real solution two irrational solutions two complex solutions that are not real two rational solutions

Solution

2x = 5x^2 - 1

rearrange : 5x^2 -2x -1 =0

discrimnant : b^2 -4ac = (2)^2 - 4*(5)*(-1) = 4 + 20 = 24

Discriminant is not perfect square so, irrational roots

So, roots of equation : x = ( 2 +/- sqrt(24) )/10 = (1 +/- 2sqrt(6) )/5

Two irrational roots

Option B