Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2-13x=0\)
2. \(9x^2+18x=7x^2+8x\)
3. \(-3x^2+11x=4x^2-4x\)
4. \(5x^2+11x=-2x^2+7x\)
5. \(-3x^2+24x=0\)
6. \(-5x^2+18x=-3x^2-5x\)
7. \(4(4x^2-7x)=-(-15x^2+3x)\)
8. \(-15x^2+30x=-8x^2+9x\)
9. \(8x^2-14x=0\)
10. \(3x^2-2x=8x^2-9x\)
11. \(8x^2-6x=10x^2-7x\)
12. \(-2x^2+0x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2-13x=0 \\ \Leftrightarrow x(2x-13) = 0 \\ \Leftrightarrow x = 0 \vee 2x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{2} \\ V = \Big\{ \frac{13}{2}; 0 \Big\} \\ -----------------\)
2. \(9x^2+18x=7x^2+8x \\ \Leftrightarrow 2x^2+10x=0 \\ \Leftrightarrow x(2x+10) = 0 \\ \Leftrightarrow x = 0 \vee 2x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{2} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
3. \(-3x^2+11x=4x^2-4x \\ \Leftrightarrow -7x^2+15x=0 \\ \Leftrightarrow x(-7x+15) = 0 \\ \Leftrightarrow x = 0 \vee -7x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-7} = \frac{15}{7} \\ V = \Big\{ \frac{15}{7}; 0 \Big\} \\ -----------------\)
4. \(5x^2+11x=-2x^2+7x \\ \Leftrightarrow 7x^2+4x=0 \\ \Leftrightarrow x(7x+4) = 0 \\ \Leftrightarrow x = 0 \vee 7x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{7} \\ V = \Big\{ 0 ; \frac{-4}{7} \Big\} \\ -----------------\)
5. \(-3x^2+24x=0 \\ \Leftrightarrow x(-3x+24) = 0 \\ \Leftrightarrow x = 0 \vee -3x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-3} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
6. \(-5x^2+18x=-3x^2-5x \\ \Leftrightarrow -2x^2+23x=0 \\ \Leftrightarrow x(-2x+23) = 0 \\ \Leftrightarrow x = 0 \vee -2x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-2} = \frac{23}{2} \\ V = \Big\{ \frac{23}{2}; 0 \Big\} \\ -----------------\)
7. \(4(4x^2-7x)=-(-15x^2+3x) \\ \Leftrightarrow 16x^2-28x=15x^2-3x \\ \Leftrightarrow 16x^2-28x-15x^2+3x= 0 \\ \Leftrightarrow x^2+25x=0 \\ \Leftrightarrow x(x+25) = 0 \\ \Leftrightarrow x = 0 \vee x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{1} = -25 \\ V = \Big\{ 0 ; -25 \Big\} \\ -----------------\)
8. \(-15x^2+30x=-8x^2+9x \\ \Leftrightarrow -7x^2+21x=0 \\ \Leftrightarrow x(-7x+21) = 0 \\ \Leftrightarrow x = 0 \vee -7x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-7} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
9. \(8x^2-14x=0 \\ \Leftrightarrow x(8x-14) = 0 \\ \Leftrightarrow x = 0 \vee 8x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{8} = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)
10. \(3x^2-2x=8x^2-9x \\ \Leftrightarrow -5x^2+7x=0 \\ \Leftrightarrow x(-5x+7) = 0 \\ \Leftrightarrow x = 0 \vee -5x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-5} = \frac{7}{5} \\ V = \Big\{ \frac{7}{5}; 0 \Big\} \\ -----------------\)
11. \(8x^2-6x=10x^2-7x \\ \Leftrightarrow -2x^2+1x=0 \\ \Leftrightarrow x(-2x+1) = 0 \\ \Leftrightarrow x = 0 \vee -2x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-2} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
12. \(-2x^2+0x=0 \\ \Leftrightarrow -2x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-2} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)