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REAL NUMBER YW show some rove Bf, , SHARE TO YOUR SCHOOLMATES, Euclid division lemma, , © Given positive integers @ and b there exist whole mumbers, 4 and r= satisfying a= bytr O<r<b, , Euclid division algoritham, , @ according to this the HCF of any any two positive integers, aand b with arb , is obtaind os follow., , Step-1 Apply the division lemma fo find 4 andr Where acbe+r, Step-2 TF r=0, the HCF is b TF #0 apply division lemma +o band r, , Step-3 Continue the process till the reminder is zero , The divisor, at the stage will be HEF (a,b) = HCF (by), , , , ( THE FUNDAMENTAL THEORM OF ARITHMETLC ), , Every composite number can be expressed (factorised) Os a product of, Primes and this factroisation is unique apast from the order in, Which the prime factors occur, , If p is a printe ond p divides 0? , then p divides a, where, a is a positive integer, , HF (a,b) X LOM (ab) = aXxb, , tl t.me / Academeasy

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POLYNOMIALS, , Degree, © Linear Polynomial 2, , 1, © Quadratic Polynomial + 2, © Cubic Polynomial » 3, , Zero of the linear polynomial, , Zerg = - Constant term _ _b, Cofficient of x a, Required polynomial, , x? - (Sum of zeros)x + product of zero, © FORMULA > 2z*- (atp)u+ ag, , Division algorithm — for polynomial, © pl) = gl) x ote) + Yi), , Tf ti) =0 ‘Wen Gx) and aia), is the factor of plx), , Application of zero of polynomial, Od+p* = (a+p) - 208, , © (@-p) = G+) -4ag, , No of Zeros Genral formula, 1 ax+b (a#o), , 2 Oy? +bx+c (a#0), 3 Ox? + be +cxz+d (#0), , , , Relationship between xero and coffictent, Of Quadratic polynomial Ox? + bx +c (a#0), , , , © sum of zeros = -b = “efficient of x, & cofficient of 22, , © Product of zeros = £ - Constant term, O& cafficient of x2, , Relationship between ero and, Coffictent of Cubic polynomial, , Osum of zero (+B +7) = -2, , ©Product of zero ( «py) = “4, , @sum of product of Zeroes taken two, at a time <= ap+ pit ya = £, , © a?-p* = re) [(ateP- Gap, , © a+p = (atp) - 3ap (a+p)