How do you find the discriminant, describe the number and type of root, and find the exact solution using the quadratic formula given $3/4x^2-1/3x-1=0$ ?

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Answer 1 · 2018-05-09T15:51:31

$Delta=1/9+3=28/9>0=> "two distinct real roots"$

$x=2/9+4/9sqrt7$
or
$x=2/9-4/9sqrt7$

for a quadratic equation

$ax^2+bx+c=0$

the discriminant is given by

$Delta=b^2-4ac---(1)$

$Delta>0=>$ two distinct real roots

$Delta=0=>$ one root (ie two equal roots)

$Delta<0=>$ two distinct complex roots( conjugate pairs if $a,b,cinRR$ )

we have

$3/4x^2-1/3x-1=0$

multiply the eqn by $12$

$a=3/4,b=-1/3, c=-1$

$(1)rarrDelta=(-1/3)^3-4(3/4)(-1)$

$Delta=1/9+3=28/9>0$

#:. two distinct real roots

#quadratic eqn

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

$x=(1/3+-sqrt(28/9))/(3/2)$

$x=(1/3+-(2sqrt7)/3)/(3/2)$

$x=2/9+-4/9sqrt7$

How do you find the discriminant, describe the number and type of root, and find the exact solution using the quadratic formula given 3/4x^2-1/3x-1=03/4x^2-1/3x-1=0?