Berekeninge
Los liniêre, kwadmatiese en stelsels van vergelykings stap stap vir stap, vry aanlyn.
Resultate werk op soos jy tik.
Aangaande hierdie sakrekenaar
An equation solver finds the values that satisfy an equation. This tool solves linear equations, quadratic equations (via the quadratic formula, including complex roots) and systems of two linear equations. Choose the type, enter the coefficients, and get the solution with the key working shown.
For a linear equation ax + b = 0 it simply rearranges to x = -b/a. For a quadratic ax² + bx + c = 0 it applies the quadratic formula, first computing the discriminant b² − 4ac: a positive discriminant gives two real roots, zero gives one repeated root, and a negative discriminant gives a pair of complex-conjugate roots which it reports rather than declaring "no solution". For a 2×2 system it solves the two lines simultaneously to find the single point where they cross.
For a worked example, solving x² − 5x + 6 = 0 gives a discriminant of 25 − 24 = 1, so the roots are x = (5 ± 1)/2, that is x = 3 and x = 2. By contrast x² + 1 = 0 has discriminant -4 and returns the complex roots x = i and x = -i. Students use it to check algebra homework, find where a parabola crosses the x-axis, or solve the pair of equations behind a word problem.
Dikwels gevra vrae
Watter soorte vergelykings kan dit oplos?
Liniêre vergelykings (ax + b = 0), kwadmatiese (ax2 + bx + c = 0, insluitend komplekse wortels) en 2×2 stelsels van lineêre vergelykings.
Is dit'n ingewikkelde oorsprong?
Ja. Wanneer'n kwawamatiese'n negatiewe diskriminant het, berig die oplosder die twee komplekse konjugasiewortels eerder as om te sê dat daar geen oplossing is nie.
How do I solve a quadratic like x² − 5x + 6 = 0?
Kies die kwadmatiese tipe en invoer 'n = 1, b = -5, c = 6. Die oploser pas die kwadmatiese formule toe en gee terug x = 2 en x = 3, die twee waardes wat maak die uitdrukking nul.
Wat is die teenstrydigheid en waarom maak dit saak?
The discriminant is b² − 4ac. If it is positive there are two real roots, if it is zero there is one repeated root, and if it is negative the roots are a complex conjugate pair. The solver uses it to decide which case applies.
Hoe los ek'n stelsel van twee vergelykings op?
Kies die 2×2 stelsel tipe en invoer die koeffisients van beide vergelykings. Die oplosder vind die enkel (x, y) punt waar die twee lyne ontmoet, of sê vir jou wanneer hulle parallelle is en nooit kruis nie.
Hoe verskil dit van die grafbeelder?
Die vergelyking oplosder gee terug Die presiese oplossing waardes apgently. Die grafieking sakrekenaar in plaas van trek die kurwes sodat jy kan sien die wortels as x-as kruising of die kruising van twee grafieke.
Die resultate is skattings van algemene leiding, nie net finansiële, mediese of belastingvoorligting nie.