Question

What is the nature of roots of (a) x^2-2√3x+3=0
(b) 4x^2-112x-9=0

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Answer 1

a) a=1, b=-2√3, c=3
$d = {b}^{2} - 4ac$
d=(-2√3)^2 -4•1•3
= 12 -12
D = 0
roots are real and equal

b) a=4, b= -112, c= -9
D = (-112)^2 -4•4•-9
= 12544 + 144
D = 12688, D>0
roots are real and distinct