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

Question

3686 views around the world

You can reuse this answer
Creative Commons License

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

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

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

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

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

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

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

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