Question

Determine the nature of the roots of the following quadratic equations:

(a) 3x^2 - 6x + 7 = 0

(b) 3x^2 + 6x - 7 = 0

(c) -5x^2- x/5 = 0

(d) 4x^2 - 28 49
----x + ----- = 0
3 9

Answer 1

b^2-4ac says it all
in (a) for example
36-4(21) is negative so sqrt of negative in sollution so complex roots

(b) 36 + 4(21) is + so real roots

(c) x^2 + x/25 = 0
x(x+1/25) = 0
x = 0 or x = -1/25

(d) ?

Answer 2

check in your text or in your notes what properties are needed to investigate the nature of the roots.
hint: it has to do with the determinant.

btw. - I can't make your your last equation.