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Query

4.10: Kupata Mizizi yote ya Real ya Kazi

  • Page ID
    164624
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    Ili kupata mizizi halisi ya kazi, tafuta ambapo kazi inakabiliana na x-axis. Ili kupata ambapo kazi intersects x-axis, kuweka\(f(x) = 0\) na kutatua equation kwa\(x\).

    Kama kazi ni kazi linear ya shahada 1,\(f(x) = mx + b\) na x-intercept ni mzizi wa equation, kupatikana kwa kutatua equation kwa\(x\). Ili kupata mizizi ya equations quadratic, kuna njia kadhaa za kupata zero:

    1. Fanya kikamilifu kujieleza kwa quadratic.
    2. Tumia formula ya quadratic, na equation ya quadratic katika fomu\(Ax^2 + Bx + C = 0\).
    3. Jaza mraba kwenye kujieleza kwa quadratic (sio pamoja na kitabu hiki).

    Baadhi ya equations za ujazo pia inaweza kutatuliwa kwa urahisi, ikiwa polynomial inaweza kuhesabiwa ili kupata zero. Pia, equation ya ujazo inaweza kuhesabiwa ikiwa imeandikwa kwa namna ya jumla au tofauti ya cubes kamilifu. Ikiwa sio fomu hii, basi calculator au kompyuta inaweza kupata mizizi ya equation ya ujazo.

    Lengo la darasa letu ni kufanya kazi na polynomials ambao mizizi inaweza kupatikana kwa kutumia mbinu za jadi za algebraic. Kwa maelezo kuhusu jinsi ya kuzingatia maneno, tafadhali rejea sehemu Factoring/Kutafuta Solutions Polynomial (zero). Kwa maelezo kuhusu jinsi ya kutumia Mfumo wa Quadratic, tafadhali rejea sehemu hiyo katika waraka.

    Pata mizizi halisi ya kila equation kwa kuzingatia au kutumia Mfumo wa Quadratic. Eleza majibu halisi ya mwisho yaliyorahisishwa (namba halisi au maneno yaliyorahisishwa makubwa).

    1. \(x ^2 + x − 12 = 0\)
    2. \(−6x ^2 + x + 12 = 0\)
    3. \(4x ^2 + 5x − 6 = 0\)
    4. \(\dfrac{1 }{2} a^2 + a − 12 = 0\)
    5. \(2x^2 + 7x − 15=0\)
    6. \(12x^2 − 9x − 3 = 0\)