Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2+12x=-9x^2-3x\)
2. \(-14x^2+19x=-8x^2+10x\)
3. \(15x^2+22x=9x^2+10x\)
4. \(-2(9x^2+7x)=-(19x^2-3x)\)
5. \(-2(-5x^2+2x)=-(-9x^2+11x)\)
6. \(-4x^2+8x=0\)
7. \(-7x^2-28x=-6x^2-5x\)
8. \(3(5x^2-4x)=-(-16x^2+28x)\)
9. \(-7x^2+23x=0\)
10. \(6x^2-4x=0\)
11. \(7x^2-9x=0\)
12. \(-2(8x^2+4x)=-(19x^2-3x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2+12x=-9x^2-3x \\ \Leftrightarrow x^2+15x=0 \\ \Leftrightarrow x(x+15) = 0 \\ \Leftrightarrow x = 0 \vee x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{1} = -15 \\ V = \Big\{ 0 ; -15 \Big\} \\ -----------------\)
2. \(-14x^2+19x=-8x^2+10x \\ \Leftrightarrow -6x^2+9x=0 \\ \Leftrightarrow x(-6x+9) = 0 \\ \Leftrightarrow x = 0 \vee -6x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-6} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
3. \(15x^2+22x=9x^2+10x \\ \Leftrightarrow 6x^2+12x=0 \\ \Leftrightarrow x(6x+12) = 0 \\ \Leftrightarrow x = 0 \vee 6x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{6} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
4. \(-2(9x^2+7x)=-(19x^2-3x) \\ \Leftrightarrow -18x^2-14x=-19x^2+3x \\ \Leftrightarrow -18x^2-14x+19x^2-3x= 0 \\ \Leftrightarrow x^2+17x=0 \\ \Leftrightarrow x(x+17) = 0 \\ \Leftrightarrow x = 0 \vee x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{1} = -17 \\ V = \Big\{ 0 ; -17 \Big\} \\ -----------------\)
5. \(-2(-5x^2+2x)=-(-9x^2+11x) \\ \Leftrightarrow 10x^2-4x=9x^2-11x \\ \Leftrightarrow 10x^2-4x-9x^2+11x= 0 \\ \Leftrightarrow x^2-7x=0 \\ \Leftrightarrow x(x-7) = 0 \\ \Leftrightarrow x = 0 \vee x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{1} = 7 \\ V = \Big\{ 7; 0 \Big\} \\ -----------------\)
6. \(-4x^2+8x=0 \\ \Leftrightarrow x(-4x+8) = 0 \\ \Leftrightarrow x = 0 \vee -4x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-4} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
7. \(-7x^2-28x=-6x^2-5x \\ \Leftrightarrow -x^2-23x=0 \\ \Leftrightarrow x(-x-23) = 0 \\ \Leftrightarrow x = 0 \vee -x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-1} = -23 \\ V = \Big\{ 0 ; -23 \Big\} \\ -----------------\)
8. \(3(5x^2-4x)=-(-16x^2+28x) \\ \Leftrightarrow 15x^2-12x=16x^2-28x \\ \Leftrightarrow 15x^2-12x-16x^2+28x= 0 \\ \Leftrightarrow -x^2-16x=0 \\ \Leftrightarrow x(-x-16) = 0 \\ \Leftrightarrow x = 0 \vee -x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-1} = -16 \\ V = \Big\{ 0 ; -16 \Big\} \\ -----------------\)
9. \(-7x^2+23x=0 \\ \Leftrightarrow x(-7x+23) = 0 \\ \Leftrightarrow x = 0 \vee -7x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-7} = \frac{23}{7} \\ V = \Big\{ \frac{23}{7}; 0 \Big\} \\ -----------------\)
10. \(6x^2-4x=0 \\ \Leftrightarrow x(6x-4) = 0 \\ \Leftrightarrow x = 0 \vee 6x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{6} = \frac{2}{3} \\ V = \Big\{ \frac{2}{3}; 0 \Big\} \\ -----------------\)
11. \(7x^2-9x=0 \\ \Leftrightarrow x(7x-9) = 0 \\ \Leftrightarrow x = 0 \vee 7x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{7} \\ V = \Big\{ \frac{9}{7}; 0 \Big\} \\ -----------------\)
12. \(-2(8x^2+4x)=-(19x^2-3x) \\ \Leftrightarrow -16x^2-8x=-19x^2+3x \\ \Leftrightarrow -16x^2-8x+19x^2-3x= 0 \\ \Leftrightarrow 3x^2+11x=0 \\ \Leftrightarrow x(3x+11) = 0 \\ \Leftrightarrow x = 0 \vee 3x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{3} \\ V = \Big\{ 0 ; \frac{-11}{3} \Big\} \\ -----------------\)