Question

20 Point!

Evaluate the discriminant for each equation, then use it to determine the nature of the roots for each quadratic equation.

(a) x^+4x+5=0

(b) x^-4x-5=0

(c) 4x^2+20x+25=0

Answer 1

determinant:
`√(b^2-4ac)`

(a)
`x^2+4x+5=0\\D=4^2-4\cdot1\cdot5={-4}\\D<0`

D<0 means there are no real roots. there are two complex roots with imaginary components.

(b) D=16+20=36>0

D>0 means there are two real roots

(c) D = 20^2-4*4*25 = 0

D=0 means there is one real root with multiplicity 2