How do you find the discriminant, describe the number and type of root, and find the exact solution using the quadratic formula given $- 3 x^{2} - 5 x + 2 = 0$ $-3x^2-5x+2=0$ ?

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Answer 1 · 2016-11-23T13:39:39

The solution is $S = {- 2, \frac{1}{3}}$ $S={-2,1/3}$

The equation is $- 3 x^{2} - 5 x + 2 = 0$ $-3x^2-5x+2=0$

The quadratic equation is $a x^{2} + b x + c = 0$ $ax^2+bx+c=0$

We start by calculating the discriminant

$Delta = b^2-4ac=(-5)^2-4(-3)(+2)$
$=25+27=49$

As, $Delta >0$ , we expect 2 real roots

The roots are
$=(-b+-sqrtDelta)/(2a)$

$x_1=(5+7)/(-6)=-2$

$x_2=(5-7)/(-6)=1/3$

How do you find the discriminant, describe the number and type of root, and find the exact solution using the quadratic formula given -3x^2-5x+2=0−3x2−5x+2=0-3x^2-5x+2=0?