Kusintha
Kuchotsa linear, quadratic ndi dongosolo la equations step by step, ufulu pa intaneti.
Zithunzizi zimasintha monga momwe mumalemba.
Zachidule
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.
Mafunso ofunsidwa nthawi zambiri
Kodi ndi mitundu iti ya equations ikhoza kukwaniritsa?
Linear equations (ax + b = 0), quadratics (ax² + bx + c = 0, including complex roots), and 2×2 systems of linear equations.
Kodi amasonyeza mbewu zosiyanasiyana?
Yes. pamene quadratic ali ndi woipa discriminant, wothamanga akudziwitsa awiri zophweka conjugate roots kuposa kunena kuti palibe njira.
Kodi ndingatani kuti ndithe kuchotsa mfundo yachiwiri ya x² − 5x + 6 = 0?
Sankhani mtundu wa squared ndi kulowa a = 1, b = -5, c = 6. The wothamanga amagwiritsa ntchito squared formula ndi kubwezera x = 2 ndi x = 3, matanthauzo awiri amene amachititsa tanthauzo zero.
Kodi ndi chiyani chosiyana ndi chiyani ndi chiyani?
Kusiyana ndi b² - 4ac. Ngati ndi woipa pali mbewu ziwiri zachilungamo, ngati ndi zero pali mbewu imodzi yopita m'mbuyo, ndipo ngati ndi yoipa mbewu ndi complex conjugate awiri. Wothamanga amagwiritsa ntchito kuti asankhe kuti ndi nkhani yoti agwiritse ntchito.
Kodi ndingatani kuti ndisinthe mfundo za m'mawu awiri?
Sankhani 2 × 2 dongosolo mtundu ndi kulowa coefficients ya onse equation. The solver amapeza imodzi (x, y) malo kumene awiri mafano kukumana, kapena akuuzani pamene iwo ndi mofanana ndi ndipo sabata kugwa.
Kodi ndi chiyani chomwe chimasiyana ndi graphing calculator?
The equation solver imabwerera mwatsatanetsatane zofunikira zoyenera algebraically. The graphing calculator pamalo amamanga ma curves kuti muthe kuona mbewu monga x-axis crossings kapena kulumikizana kwa ma graph awiri.
Zimenezi ndi zowerengera zokhudzana ndi malangizo amtundu uliwonse, si zokhudzana ndi ndalama, zamoyo kapena zokhudzana ndi ndalama.