How do you find the discriminant, describe the number and type of root, and find the exact solution using the quadratic formula given #x^2+4x+3=0#?

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Answer 1 · 2017-03-06T16:17:23

#Delta=16-12=4>0#

#: ."the quadratic has two unequal real roots".#

#x=-1,-3#

#"For the quadratic equation "ax^2+bx+c=0#

#"the discriminant "Delta=b^2-4ac#

#Delta>0=>"two unequal real roots"#

#Delta=0=>"two equal roots"#

#Delta<0=>" complex roots "#

#x^2+4x+3=0#

#a=1,b=4, c=3#

#Delta=4^2-4xx1xx3#

#Delta=16-12=4>0#

#: ."the quadratic has two unequal real roots".#

solving with formula

#x^2+4x+3=0#

#x=(-b+-sqrtDelta)/(2a)#

#x=(-4+-sqrt4)/2#

#x=(-4+-2)/2#

#x_1=(-4+2)/2=-1#

#x_2=(-4-2)/2=-3#