a) x²-7x-8<0 Δ=(-7)²-4*1*(-8) Δ=49+32 Δ=81 √Δ=9 x₁=(-(-7)-9)/(2*1) x₁=-2/2 x₁=-1 x₂=(-(-7)+9)/(2*1) x₂=16/2 x₂=8 X∈(-1,8) b) -3x2+8x+5 ≥0 Δ=8²-4*(-3)*5 Δ=64+60 Δ=124 √Δ=2√31 x₁=(-8-2√31)/(2*(-3)) x₁=(-8-2√31)/-6 x₁=4/3-√31/3 x₂=(-8+2√31)/(2*(-3)) x₂=(-8+2√31)/-6 x₂=4/3+√31/3 x∈<4/3-√31/3,4/3+√31/3> 2. a) x³-3x²-4x+12=0 x²(x-3)-4(x-3)=0 (x²-4)(x-3)=0 x²-4=0 x²=4 x=-2 ∨ x=2 x-3=0 x=3 3. Załącznik
1. a) x2 - 7x - 8 < 0 D = 49 +32 =81 VD =9 X1 =(7-9)/2 X1 = -1 X2 =(7+9)/2 X2 = 8 X e (-1;8) b) -3x2 +8x +5 >= 0 D =64 +60 =124 VD =V124 =2V31 X1 =(-8 -2V31)/(-6) X1 =4/3 +V31/3 X2 =(-8 +2V31)/(-6) X2 =4/3 -V31/3 X e < 4/3-V31/3; 4/3+V3/3 > 2. x3 -3x2 -4x +12 = 0 x2(x-3) -4(x-3) = 0 (x-3)(x2 -4) = 0 x-3 = 0 lub x2-4 = 0 x-3 = 0 x =3 x2 -4 =0 (x+2)(x-2) = 0 x = -2 x = 2 {x =-2} {x =2} {x =3} 3. (3x3 -2x2 -x -5):(x-3) =3x2 +7x +20 -3x3 +9x2 --------------- ------ -7x2 -x ------ -7x2+21x -------------------- ------------- 20x-5 ------------ -20x+60 ------------------------ -------------- = 55 (3x2 +7x +20)(x-3) +55
