Question

Prove that equation 6x^2 + 5x - 4 = 0 does not have equal roots and roots are rational

Answer 1

6x²+5x-4

It's discriminant is given by,

$d = \sqrt{ {b}^{2} - 4ac} \\ = \sqrt{ {5}^{2} - 4(6)( - 4) } \\ = \sqrt{25 + 96} = \sqrt{121} = 11$

Since, the discriminant is drafter than zero, i.e., D > 0 therefore it's roots will not be equal and they are rational.