Equation Solver
Solve linear, quadratic uye system of equations nhanho nenzira, free online.
Zvinyorwa zvinogadziridzwa paunenge uchinyora.
Nezve iyi kalkulator
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.
Zvimwe zvinobvunzwa zvakanyanya
Ndezvipi zvimiro zveequations zvinokwanisa kugadziriswa?
Equations linear (ax + b = 0), quadratics (ax² + bx + c = 0, kusanganisira rusununguko zvakaoma), uye 2 × 2 system of linear equations.
Inoratidza sei ma roots akaoma?
Kana quadratic ane chikonzero chakaipa discriminant, solver anotaura maviri zvakaoma conjugate roots kupfuura kutaura hapana mhinduro.
Ndeupi mubvunzo watinoda kubvunza kuti x² − 5x + 6 = 0?
Choose the quadratic type and enter a = 1, b = -5, c = 6. The solver applies the quadratic formula and returns x = 2 and x = 3, the two values that make the expression zero.
Chii chinonzi discriminant uye nei ichikosha?
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.
Maitiro ekubvisa zvinyorwa kubva kune imwe system yezvinyorwa?
Kusarudza 2 × 2 system type uye nyora coefficients yezviuru zve equation. The solver finds the single (x, y) point where the two lines meet, or tells you when they are parallel and never cross.
Sei izvi zvakasiyana ne graphing calculator?
The equation solver returns the exact solution values algebraically. The graphing calculator instead draws the curves so you can see the roots as x-axis crossings or the intersection of two graphs.
Zviratidzo zvemubvunzo ndezvekufungidzira kwechinangwa chekudzidzisa chete, kwete zvemari, zvehutano kana zvemari.