Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(8x^2-17x=0\)
2. \(13x^2-x=10x^2-10x\)
3. \(5(8x^2+8x)=-(-36x^2-21x)\)
4. \(11x^2-18x=7x^2-5x\)
5. \(15x^2+7x=10x^2+4x\)
6. \(-7x^2+17x=0\)
7. \(-8x^2-24x=0\)
8. \(-4x^2+12x=0\)
9. \(-4x^2-8x=-10x^2-2x\)
10. \(-15x^2-5x=-8x^2+5x\)
11. \(7x^2-24x=0\)
12. \(4x^2+14x=-2x^2+5x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(8x^2-17x=0 \\ \Leftrightarrow x(8x-17) = 0 \\ \Leftrightarrow x = 0 \vee 8x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{8} \\ V = \Big\{ \frac{17}{8}; 0 \Big\} \\ -----------------\)
2. \(13x^2-x=10x^2-10x \\ \Leftrightarrow 3x^2+9x=0 \\ \Leftrightarrow x(3x+9) = 0 \\ \Leftrightarrow x = 0 \vee 3x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{3} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
3. \(5(8x^2+8x)=-(-36x^2-21x) \\ \Leftrightarrow 40x^2+40x=36x^2+21x \\ \Leftrightarrow 40x^2+40x-36x^2-21x= 0 \\ \Leftrightarrow 4x^2-19x=0 \\ \Leftrightarrow x(4x-19) = 0 \\ \Leftrightarrow x = 0 \vee 4x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{4} \\ V = \Big\{ \frac{19}{4}; 0 \Big\} \\ -----------------\)
4. \(11x^2-18x=7x^2-5x \\ \Leftrightarrow 4x^2-13x=0 \\ \Leftrightarrow x(4x-13) = 0 \\ \Leftrightarrow x = 0 \vee 4x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{4} \\ V = \Big\{ \frac{13}{4}; 0 \Big\} \\ -----------------\)
5. \(15x^2+7x=10x^2+4x \\ \Leftrightarrow 5x^2+3x=0 \\ \Leftrightarrow x(5x+3) = 0 \\ \Leftrightarrow x = 0 \vee 5x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{5} \\ V = \Big\{ 0 ; \frac{-3}{5} \Big\} \\ -----------------\)
6. \(-7x^2+17x=0 \\ \Leftrightarrow x(-7x+17) = 0 \\ \Leftrightarrow x = 0 \vee -7x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-7} = \frac{17}{7} \\ V = \Big\{ \frac{17}{7}; 0 \Big\} \\ -----------------\)
7. \(-8x^2-24x=0 \\ \Leftrightarrow x(-8x-24) = 0 \\ \Leftrightarrow x = 0 \vee -8x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-8} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
8. \(-4x^2+12x=0 \\ \Leftrightarrow x(-4x+12) = 0 \\ \Leftrightarrow x = 0 \vee -4x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{-4} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
9. \(-4x^2-8x=-10x^2-2x \\ \Leftrightarrow 6x^2-6x=0 \\ \Leftrightarrow x(6x-6) = 0 \\ \Leftrightarrow x = 0 \vee 6x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{6} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
10. \(-15x^2-5x=-8x^2+5x \\ \Leftrightarrow -7x^2-10x=0 \\ \Leftrightarrow x(-7x-10) = 0 \\ \Leftrightarrow x = 0 \vee -7x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-7} = \frac{-10}{7} \\ V = \Big\{ 0 ; \frac{-10}{7} \Big\} \\ -----------------\)
11. \(7x^2-24x=0 \\ \Leftrightarrow x(7x-24) = 0 \\ \Leftrightarrow x = 0 \vee 7x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{7} \\ V = \Big\{ \frac{24}{7}; 0 \Big\} \\ -----------------\)
12. \(4x^2+14x=-2x^2+5x \\ \Leftrightarrow 6x^2+9x=0 \\ \Leftrightarrow x(6x+9) = 0 \\ \Leftrightarrow x = 0 \vee 6x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{6} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)