1) 3 x^3 + 3 x^2 - 2 x = 0 x*( 3 x^2 + 3 x - 2 ) =0 x 1= 0 lub 3 x^2 + 3 x - 2 = 0 delta = 3^2 - 4*3*(-2) = 9 + 24 = 33 p( delty) = p(33) więc x2 = ( - 3 - p(33))/ 6 = - 0,5 - p(33)/6 x3 = ( - 3 + p(33))/ 6 = - 0,5 + p(33)/6 ============================= 2) 2 x^4 - 8 x^3 + 6 x^2 = 0 x^2 * ( 2 x^2 - 8 x + 6 ) = 0 x^2 = 0 lub 2 x^2 - 8 x + 6 = 0 x1 = 0 ======== delta = ( -8)^2 - 4*2*6 = 64 - 48 = 16 p( delty ) = 4 x2 = ( 8 - 4)/ 4 = 1 x3 = ( 8 + 4)/ 4 = 3 ================ 3) 5 x^2 + 2 x^4 + x^3 = 0 x^2 * ( 5 + 2 x^2 + x ) = 0 x^2 = 0 lub 2 x^2 + x + 5 = 0 x1 = 0 ==== delta = 1^2 - 4*2*5 = 1 - 40 < 0 - brak innych pierwiastków rzeczywistych Odp. x = 0 ======== 4) -2 x^3 - 6 x^2 + 8 x = 0 x*( -2 x^2 - 6 x + 8 ) = 0 x = 0 lub - 2 x^2 - 6 x + 8 = 0 x1 = 0 delta = ( -6)^2 - 4*(-2)*8 = 36 + 64 = 100 p (delty) = 10 x2 = ( 6 - 10)/ ( -4) = 1 x3 = ( 6 + 10) / ( -4) = - 4 =================== 5) x^5 - 7 x^4 + 12 x^3 = 0 x^3 *( x^2 - 7 x + 12 ) = 0 x^3 = 0 lub x^2 - 7 x + 12 = 0 x1 = 0 ===== delta = (-7)^2 - 4*1*12 = 49 - 48 = 1 x2 = ( 7 - 1)/2 = 3 x3 = ( 7 + 1)/ 2 = 4 =============== 6) x^4 + 18 x^2 = 9 x^3 x^2 *( x^2 - 9 x + 18 ) = 0 x^2 = 0 lub x^2 - 9 x + 18 = 0 x1 = 0 ==== delta = ( -9)^2 - 4*1*18 = 81 - 72 = 9 p( delty ) = 3 x2 = ( 9 - 3)/ 2 = 3 x3 = ( 9 + 3)/2 = 6 ================= 7 ) 2 x^4 + 8 x^3 = x^5 x^5 - 2 x^4 - 8 x^3 = 0 x^3 *( x^2 - 2 x - 8 ) = 0 x^3 = 0 lub x^2 - 2 x - 8 = 0 x1 = 0 ===== delta = ( -2)^2 - 4*1*(-8) = 4 + 32 = 36 p( delty ) = 6 x2 = ( 2 - 6)/ 2 = - 4/2 = - 2 x3 = ( 2 + 6)/2 = 8/2 = 4 ==================
