<h4>1. Zapiši kao kvadrat binoma:</h4> <p>a) \(4x^2 + 12x + 9 = §§V0(-10,10,1)§§x^2 + §§V1(-20,20,1)§§x + 9\)</p> <p>b) \(9x^2 - 12x + 4 = §§V2(-10,10,1)§§x^2 - §§V3(-20,20,1)§§x + 4\)</p> <p>c) \(4x^2 - 20x + 25 = §§V4(-10,10,1)§§x^2 - §§V5(-20,20,1)§§x + 25\)</p> <p>d) \(25x^2 - 40x + 16 = §§V6(-10,10,1)§§x^2 - §§V7(-20,20,1)§§x + 16\)</p> <h4>2. Ako znaš da se dati trinom može napisati u obliku \( (Ax + B)^2 \), odredi vrijednosti A i B.</h4> <p>a) \(B = §§V0(-5,5,1)§§, A = (§§V1(-10,10,1)§§)^2 \) => \( (§§V0(-5,5,1)§§x)^2 + 2(§§V0(-5,5,1)§§x) + (§§V1(-10,10,1)§§)^2 = (§§V0(-5,5,1)§§x + §§V1(-10,10,1)§§)^2 \)</p> <p>b) \(B = §§V2(5,15,5)§§, A = (§§V3(-5,5,1)§§)^2 \) => \( (§§V2(5,15,5)§§x)^2 + 2(§§V2(5,15,5)§§x) + (§§V3(-5,5,1)§§)^2 = (§§V2(5,15,5)§§x + §§V3(-5,5,1)§§)^2 \)</p> <h4>3. Zapiši kao kvadrat binoma:</h4> <p>a) \(6x^2 + 18x + 9 = (§§V4(2,8,2)§§x + §§V5(1,5,1)§§)^2\)</p> <p>b) \(25x^2 - 20x + 4 = (§§V6(-5,5,1)§§x - §§V7(-2,2,0.5)§§)^2\)</p> <p>c) \(16x^2 - 16x + 4 = (§§V8(-4,4,1)§§x - §§V9(2,8,2)§§)^2\)</p> <p>d) \(9x^2 + 36x + 36 = (§§V10(-3,3,1)§§x + §§V11(6,12,1)§§)^2\)</p> <h4>4. Odredi broj a za koji je polinom kvadrat binoma:</h4> <p>a) \(§§V12(1,5,1)§§x^2 + 8x + 16, \; a = (§§V13(2,8,2)§§)^2\)</p> <p>b) \(2x^2 - 10x + 25, \; a = (§§V14(0.5,2,0.1)§§)^2\)</p> <p>c) \(§§V15(1,5,1)§§x^2 - 4xy + y^2, \; a = (§§V16(1,5,1)§§)^2\)</p> <p>d) \(§§V17(2,8,2)§§x^2 - 6xyz + 9y^2z^2, \; a = (§§V18(1,5,1)§§)^2\)</p> <p>e) \(x^2 + 6ax + 9a^2, \; a = (§§V19(2,8,2)§§)^2\)</p> <p>f) \(x^2 + 2ax + 4a^2, \; a = (§§V20(1,5,1)§§)^2\)</p> <p>g) \(9x^2 + 6ax + a^2, \; a = (§§V21(0.5,2,0.1)§§)^2\)</p> <h4>5. Zapiši kao kvadrat binoma:</h4> <p>a) \(16x^2 - 40x + 25 = (§§V22(2,8,2)§§x - §§V23(5,15,5)§§)^2\)</p> <p>b) \(9x^2 + 24xy + 16y^2 = (§§V24(3,9,3)§§x + §§V25(4,12,4)§§y)^2\)</p> <p>c) \(25x^2 + 30xy + 9y^2 = (§§V26(5,15,5)§§x + §§V27(3,9,3)§§y)^2\)</p> <p>d) \(4a^2 + 4ab + b^2 = (§§V28(2,8,2)§§a + §§V29(1,5,1)§§b)^2\)</p> <h4>6. Ako znaš da se dati trinom može napisati u obliku \( (Ax + B)^2 \), odredi vrijednosti A i B.</h4> <p>a) \(B = §§V30(4,16,4)§§, A = (§§V31(2,8,2)§§)^2 \) => \( (§§V30(4,16,4)§§x)^2 + 2(§§V30(4,16,4)§§x) + (§§V31(2,8,2)§§)^2 = (§§V30(4,16,4)§§x + §§V31(2,8,2)§§)^2 \)</p> <p>b) \(B = §§V32(-3,3,1)§§, A = (§§V33(2,8,2)§§)^2 \) => \( (§§V32(-3,3,1)§§x)^2 + 2(§§V32(-3,3,1)§§x) + (§§V33(2,8,2)§§)^2 = (§§V32(-3,3,1)§§x + §§V33(2,8,2)§§)^2 \)</p> <h4>7. Zapiši kao kvadrat binoma:</h4> <p>a) \(0.04x^2 + 0.24x + 0.36 = (§§V34(0.2,0.8,0.2)§§x + §§V35(0.6,2.4,0.6)§§)^2\)</p> <p>b) \(0.16x^2 - 0.8x + 1 = (§§V36(0.4,1.6,0.4)§§x - §§V37(1,4,1)§§)^2\)</p> <p>c) \(0.09x^2 - 0.36x + 0.36 = (§§V38(0.3,1.2,0.3)§§x - §§V39(0.6,2.4,0.6)§§)^2\)</p> <p>d) \(1.69x^2 - 2.96x + 1.44 = (§§V40(1.3,5.2,1.3)§§x - §§V41(1.2,4.8,1.2)§§)^2\)</p> <h4>8. Odredi broj a za koji je polinom kvadrat binoma:</h4> <p>a) \(§§V42(4,16,4)§§x^2 + 8x + 16, \; a = (§§V43(2,8,2)§§)^2\)</p> <p>b) \(2ax^2 - 10x + 25, \; a = (§§V44(0.5,2,0.1)§§)^2\)</p> <p>c) \(§§V45(1,5,1)§§x^2 - 4xy + y^2, \; a = (§§V46(1,5,1)§§)^2\)</p> <p>d) \(§§V47(2,8,2)§§x^2 - 6xyz + 9y^2z^2, \; a = (§§V48(1,5,1)§§)^2\)</p> <p>e) \(x^2 + 6ax + 9a^2, \; a = (§§V49(2,8,2)§§)^2\)</p> <p>f) \(x^2 + 2ax + 4a^2, \; a = (§§V50(1,5,1)§§)^2\)</p> <p>g) \(9x^2 + 6ax + a^2, \; a = (§§V51(0.5,2,0.1)§§)^2\)</p> <h4>8. Odredi broj a za koji je polinom kvadrat binoma:</h4> <p>a) \(§§V42(4,16,4)§§x^2 + 8x + 16, \; a = (§§V43(2,8,2)§§)^2 = 16\)</p> <p>b) \(2ax^2 - 10x + 25, \; a = (§§V44(0.5,2,0.1)§§)^2 = 0.25\)</p> <p>c) \(§§V45(1,5,1)§§x^2 - 4xy + y^2, \; a = (§§V46(1,5,1)§§)^2 = 1\)</p> <p>d) \(§§V47(2,8,2)§§x^2 - 6xyz + 9y^2z^2, \; a = (§§V48(1,5,1)§§)^2 = 1\)</p> <p>e) \(x^2 + 6ax + 9a^2, \; a = (§§V49(2,8,2)§§)^2 = 16\)</p> <p>f) \(x^2 + 2ax + 4a^2, \; a = (§§V50(1,5,1)§§)^2 = 1\)</p> <p>g) \(9x^2 + 6ax + a^2, \; a = (§§V51(0.5,2,0.1)§§)^2 = 0.25\)</p>