How do you find the discriminant and how many and what type of solutions does $7 x^{2} + 8 x + 1 = 0$ $7x^2+8x+1=0$ have?

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Answer 1 · 2015-05-05T07:46:31

The equation is of the form $a x^{2} + b x + c = 0$ $color(blue)(ax^2+bx+c=0$ where:

$a = 7, b = 8, c = 1$ $a=7, b=8, c=1$

The Disciminant is given by :
$Delta=b^2-4*a*c$
$= (8)^2-(4*7*1)$
$= 64-28=36$

If $Delta=0$ then there is only one solution.
(for $Delta>0$ there are two solutions,
for $Delta<0$ there are no real solutions)

As $Delta = 36$ , this equation has TWO REAL SOLUTIONS

Note :
The solutions are normally found using the formula
$x=(-b+-sqrtDelta)/(2*a)$

As $Delta = 36$ , $x = (-(8)+-sqrt36)/(2*7) = (-8+-6)/(2*7) = -2/14 or -14/14 = -1/7 or -1$

$x = -1/7,-1$ are the two solutions

How do you find the discriminant and how many and what type of solutions does 7x^2+8x+1=07x2+8x+1=07x^2+8x+1=0 have?