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=…

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asked Mar 5, 2019 139k views

1 Answer

Nathan White · Answer 1 · 2019-03-11T02:13:14+0000

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