Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

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

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2-5x=0 \\ \Leftrightarrow x(4x-5) = 0 \\ \Leftrightarrow x = 0 \vee 4x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
2. \(x^2-24x=0 \\ \Leftrightarrow x(x-24) = 0 \\ \Leftrightarrow x = 0 \vee x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{1} = 24 \\ V = \Big\{ 24; 0 \Big\} \\ -----------------\)
3. \(4(-2x^2+5x)=-(9x^2-17x) \\ \Leftrightarrow -8x^2+20x=-9x^2+17x \\ \Leftrightarrow -8x^2+20x+9x^2-17x= 0 \\ \Leftrightarrow x^2-3x=0 \\ \Leftrightarrow x(x-3) = 0 \\ \Leftrightarrow x = 0 \vee x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{1} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
4. \(2(4x^2+9x)=-(-15x^2-6x) \\ \Leftrightarrow 8x^2+18x=15x^2+6x \\ \Leftrightarrow 8x^2+18x-15x^2-6x= 0 \\ \Leftrightarrow -7x^2-12x=0 \\ \Leftrightarrow x(-7x-12) = 0 \\ \Leftrightarrow x = 0 \vee -7x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-7} = \frac{-12}{7} \\ V = \Big\{ 0 ; \frac{-12}{7} \Big\} \\ -----------------\)
5. \(-2(9x^2+6x)=-(24x^2+4x) \\ \Leftrightarrow -18x^2-12x=-24x^2-4x \\ \Leftrightarrow -18x^2-12x+24x^2+4x= 0 \\ \Leftrightarrow 6x^2+8x=0 \\ \Leftrightarrow x(6x+8) = 0 \\ \Leftrightarrow x = 0 \vee 6x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{6} = \frac{-4}{3} \\ V = \Big\{ 0 ; \frac{-4}{3} \Big\} \\ -----------------\)
6. \(13x^2+9x=7x^2-9x \\ \Leftrightarrow 6x^2+18x=0 \\ \Leftrightarrow x(6x+18) = 0 \\ \Leftrightarrow x = 0 \vee 6x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{6} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
7. \(3x^2-11x=-3x^2+3x \\ \Leftrightarrow 6x^2-14x=0 \\ \Leftrightarrow x(6x-14) = 0 \\ \Leftrightarrow x = 0 \vee 6x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{6} = \frac{7}{3} \\ V = \Big\{ \frac{7}{3}; 0 \Big\} \\ -----------------\)
8. \(-6x^2-17x=-4x^2-5x \\ \Leftrightarrow -2x^2-12x=0 \\ \Leftrightarrow x(-2x-12) = 0 \\ \Leftrightarrow x = 0 \vee -2x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-2} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
9. \(5x^2+0x=0 \\ \Leftrightarrow 5x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{5} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-6x^2-x=-2x^2+4x \\ \Leftrightarrow -4x^2-5x=0 \\ \Leftrightarrow x(-4x-5) = 0 \\ \Leftrightarrow x = 0 \vee -4x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-4} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
11. \(-3x^2-18x=0 \\ \Leftrightarrow x(-3x-18) = 0 \\ \Leftrightarrow x = 0 \vee -3x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-3} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
12. \(-9x^2+x=-2x^2-2x \\ \Leftrightarrow -7x^2+3x=0 \\ \Leftrightarrow x(-7x+3) = 0 \\ \Leftrightarrow x = 0 \vee -7x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-7} = \frac{3}{7} \\ V = \Big\{ \frac{3}{7}; 0 \Big\} \\ -----------------\)