Quadratic Equation Shot notes, Cheat Sheet of Mathematics

Download Quadratic Equation Shot notes and more Cheat Sheet Mathematics in PDF only on Docsity!

QMonoratre E@vst rons NOTES pat] cohere 040° and [o,»,cé R] (0x7 4px +¢=0) (ato). S$. Then hey are, ===, a a = oe :] and [b°-4ac]= ptacrfminont. ; ; & Muosrome Eenasne foo ps fri OSE Equation t [x* - (sum OP roots) + (Product of coors) =o] — tS 2 (b°-4ac=D)— Exists 8 condiHone t f — (Rear and distinct roots) Here (2) comes that 18, imaginary i) [D=6] — (Reat and Equat roots HamMbers [Er 7 iti) [Do— upward Parghoig rely]. Graph TS Pardboia? ii) 1p a0) Then: Range 1g (2. Bo}. <—~ if (a<0) Then Range 1S % (-0o, =| 4a fcx)= ax*+p24¢ f o a PEE | ¥ Analysis of Graph rf pee @p70] Then’ ; — Real and 1) If a0,p0,D=0 (Real and If a0 —@® v) Both roots less then k* Conditions $- sae a) DZO -b)—b LK 20 (case v) —> Jate)so Vid(of < k) and (B >) ¢ conditiong! uk -POKI <0. (cnse wr) = a- FC) vit) Exactly one root tiex between Ki and ka ¢ i Ones vit) Both, roots lying between Ky and Ks . y conditions £ “gD20. CAS 4 K, K 6) a-FCK 20-8 © wT) @—s)— k,< ~blag< kr. > S30: forpso-@° P(A <,) and(F >): 1 conditiong +- . 7 a a-Ptx,) <0 —O ST CASE ) ae i a. fCv2) <0 —@). ?, ee a iv) Both roots Greater @r then K* (case w)