How to stop quadratic formula calculator from giving inverse outputs?

Question

Alice 2024-5-30

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2124091-how-to-stop-quadratic-formula-calculator-from-giving-inverse-outputs

评论： John D'Errico 2024-6-10

Hi, I'm doing a worksheet based around matlab which involved solving quadratic formulas. I probably overcomplicated it and now made a calculator that keeps giving the inverse of my expected answer, could anyone help please?

for k = 1 : 7
disp ( ' For the equation ax^2 + bx + c ' )
a = input ( ' Enter a; ' );
b = input ( ' Enter b; ' );
c = input ( ' Enter c; ' );
D = ( b^2 ) - ( 4 * a * c );
if D < 0
fprintf ( ' \n The equation has no real roots . \n\n ')
elseif D == 0
root = -b / ( 2 * a );
fprintf ( ' \nThe equation has one root, \n ' )
fprintf ( ' %.7f\n\n ' , root )
else 
r1 = ( - b + sqrt ( D ) ) / ( 2 * a ) ;
r2 = ( - b - sqrt ( D ) ) / ( 2 * a ) ;
fprintf ( '\n The equation has two roots, \n ' ) 
fprintf ( ' %.7f and %.7f\n\n ' , r1 ,r2 ) 
end 
end
For the equation ax^2 + bx + c 
 Enter a; 
1
 Enter b; 
9
 Enter c; 
14
 The equation has two roots, 
  -2.0000000 and -7.0000000
  For the equation ax^2 + bx + c 
 Enter a; 
1
 Enter b; 
-3
 Enter c; 
-18
 The equation has two roots, 
  6.0000000 and -3.0000000

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Alice 2024-6-6

在 MATLAB Online 中打开

on the first one it was this that was inversed, as i expected two positive roots. im an absolute beginner with this sorry

Enter a;
1
Enter b;
9
Enter c;
14
The equation has two roots, 
  -2.0000000 and -7.0000000

Alice 2024-6-6

nevermind, just realised my sleep deprived misconception, sorry !

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Answer 1

John D'Errico 2024-5-30

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2124091-how-to-stop-quadratic-formula-calculator-from-giving-inverse-outputs#answer_1465556

编辑：John D'Errico 2024-5-30

在 MATLAB Online 中打开

The roots of the quadratic you supply are indeed 6 and -3.

roots([1 -3 -18])
ans = 2x1
    6.0000
   -3.0000
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So your code worked correctly.

If you expected something else, then it is your expectations that are wrong, not your code.

Anyway, perhaps I should point out that a cute feature of polynomial equations in that if you reverse the sequence of the cofficients, thus as here...

roots([-18 -3 1])
ans = 2x1
   -0.3333
    0.1667
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then the computed roots will be the inverses of the true roots. And that is what I think has happened to you in some way. This would be true for any order polynomial, in fact.

Perhaps that is what you did at some point in your code, or maybe in your spreadsheet, you provided the coefficients in the reverse order. Can we know what you actually did wrong, since your code works correctly? Only da shadow know, but I'm going to bet, that IF you have gotten the inverse of the expected roots, then somewhere, somehow, you flipped the sequence of the coefficients. I'm not da shadow though.

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Alice 2024-6-6

nevermind, just realised my sleep deprived misconception, sorry !

John D'Errico 2024-6-10

Lol. An intersting fact about an equation like

x^2 + 14*x + 9

is if ALL of the coefficients are positive, then there can NEVER be any positive real roots. Any real roots must either be zero or negative, and zero only happens if there is a zero constant term.

(You can prove that easily enough if you think about it.) For a positive root to exist, at least SOME of the coefficients must be negative.

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