Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2-11x=3x^2-6x\)
2. \(-3x^2-14x=0\)
3. \(-3(-4x^2-6x)=-(-15x^2-38x)\)
4. \(3x^2+9x=7x^2+6x\)
5. \(-5(6x^2+7x)=-(31x^2+38x)\)
6. \(15x^2+6x=10x^2+8x\)
7. \(-5(-6x^2+6x)=-(-25x^2+30x)\)
8. \(-3x^2-21x=0\)
9. \(9x^2+30x=5x^2+10x\)
10. \(-3x^2-25x=0\)
11. \(5x^2-21x=0\)
12. \(-2x^2+13x=5x^2-3x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2-11x=3x^2-6x \\ \Leftrightarrow 4x^2-5x=0 \\ \Leftrightarrow x(4x-5) = 0 \\ \Leftrightarrow x = 0 \vee 4x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
2. \(-3x^2-14x=0 \\ \Leftrightarrow x(-3x-14) = 0 \\ \Leftrightarrow x = 0 \vee -3x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-3} = \frac{-14}{3} \\ V = \Big\{ 0 ; \frac{-14}{3} \Big\} \\ -----------------\)
3. \(-3(-4x^2-6x)=-(-15x^2-38x) \\ \Leftrightarrow 12x^2+18x=15x^2+38x \\ \Leftrightarrow 12x^2+18x-15x^2-38x= 0 \\ \Leftrightarrow -3x^2+20x=0 \\ \Leftrightarrow x(-3x+20) = 0 \\ \Leftrightarrow x = 0 \vee -3x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-3} = \frac{20}{3} \\ V = \Big\{ \frac{20}{3}; 0 \Big\} \\ -----------------\)
4. \(3x^2+9x=7x^2+6x \\ \Leftrightarrow -4x^2+3x=0 \\ \Leftrightarrow x(-4x+3) = 0 \\ \Leftrightarrow x = 0 \vee -4x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-4} = \frac{3}{4} \\ V = \Big\{ \frac{3}{4}; 0 \Big\} \\ -----------------\)
5. \(-5(6x^2+7x)=-(31x^2+38x) \\ \Leftrightarrow -30x^2-35x=-31x^2-38x \\ \Leftrightarrow -30x^2-35x+31x^2+38x= 0 \\ \Leftrightarrow x^2-3x=0 \\ \Leftrightarrow x(x-3) = 0 \\ \Leftrightarrow x = 0 \vee x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{1} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
6. \(15x^2+6x=10x^2+8x \\ \Leftrightarrow 5x^2-2x=0 \\ \Leftrightarrow x(5x-2) = 0 \\ \Leftrightarrow x = 0 \vee 5x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{5} \\ V = \Big\{ \frac{2}{5}; 0 \Big\} \\ -----------------\)
7. \(-5(-6x^2+6x)=-(-25x^2+30x) \\ \Leftrightarrow 30x^2-30x=25x^2-30x \\ \Leftrightarrow 30x^2-30x-25x^2+30x= 0 \\ \Leftrightarrow 5x^2+0x=0 \\ \Leftrightarrow 5x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{5} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-3x^2-21x=0 \\ \Leftrightarrow x(-3x-21) = 0 \\ \Leftrightarrow x = 0 \vee -3x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-3} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)
9. \(9x^2+30x=5x^2+10x \\ \Leftrightarrow 4x^2+20x=0 \\ \Leftrightarrow x(4x+20) = 0 \\ \Leftrightarrow x = 0 \vee 4x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{4} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
10. \(-3x^2-25x=0 \\ \Leftrightarrow x(-3x-25) = 0 \\ \Leftrightarrow x = 0 \vee -3x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-3} = \frac{-25}{3} \\ V = \Big\{ 0 ; \frac{-25}{3} \Big\} \\ -----------------\)
11. \(5x^2-21x=0 \\ \Leftrightarrow x(5x-21) = 0 \\ \Leftrightarrow x = 0 \vee 5x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{5} \\ V = \Big\{ \frac{21}{5}; 0 \Big\} \\ -----------------\)
12. \(-2x^2+13x=5x^2-3x \\ \Leftrightarrow -7x^2+16x=0 \\ \Leftrightarrow x(-7x+16) = 0 \\ \Leftrightarrow x = 0 \vee -7x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-7} = \frac{16}{7} \\ V = \Big\{ \frac{16}{7}; 0 \Big\} \\ -----------------\)