Roots of a quadratic function: Difference between revisions

=={{header|RPL}}==

RPL can solve quadratic functions directly :

'x^2-1E9*x+1' 'x' QUAD

returns

1: '(1000000000+s1*1000000000)/2'

which can then be turned into roots by storing 1 or -1 in the <code>s1</code> variable and evaluating the formula:

DUP 1 's1' STO EVAL SWAP -1 's1' STO EVAL

hence returning

2: 1000000000

1: 0

So let's implement the algorithm proposed by the task:

{| class="wikitable"

! RPL code

! Comment

|-

|

≪

'''IF''' DUP TYPE 1 == '''THEN'''

'''IF''' DUP IM NOT '''THEN''' RE '''END END'''

≫ '<span style="color:blue">REALZ</span>' STO

.

≪ → a b c

≪ '''IF''' b NOT '''THEN''' c a / NEG √ DUP NEG '''ELSE'''

a c * √ b /

1 SWAP SQ 4 * - √ 2 / 0.5 +

b * NEG

DUP a / <span style="color:blue">REALZ</span>

c ROT / <span style="color:blue">REALZ</span> '''END'''

≫ ≫ '<span style="color:blue">QROOT</span>' STO

|

<span style="color:blue">REALZ</span> ''( number → number )''

if number is a complex

with no imaginary part, then turn it into a real

<span style="color:blue">QROOT</span> ''( a b c → r1 r2 ) ''

if b=0 then roots are obvious, else

q = sqrt(a*c)/b

f = 1/2+sqrt(1-4*q^2)/2

get -b*f

root1 = -b/a*f

root2 = -c/(b*f)

|}

1 -1E9 1 <span style="color:blue">QROOT</span>

actually returns a more correct answer:

2: 1000000000

1: .000000001