Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(7x^2-4x)=-(-27x^2-9x)\)
2. \(-6x^2+0x=0\)
3. \(6x^2-14x=0\)
4. \(2x^2+7x=4x^2+9x\)
5. \(-7x^2-20x=0\)
6. \(6x^2-1x=0\)
7. \(3(8x^2+5x)=-(-31x^2-31x)\)
8. \(-2x^2+5x=0\)
9. \(10x^2+8x=8x^2-7x\)
10. \(-8x^2-6x=-2x^2-5x\)
11. \(10x^2+13x=4x^2+8x\)
12. \(-3(8x^2+2x)=-(21x^2+13x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(7x^2-4x)=-(-27x^2-9x) \\ \Leftrightarrow 28x^2-16x=27x^2+9x \\ \Leftrightarrow 28x^2-16x-27x^2-9x= 0 \\ \Leftrightarrow x^2+25x=0 \\ \Leftrightarrow x(x+25) = 0 \\ \Leftrightarrow x = 0 \vee x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{1} = -25 \\ V = \Big\{ 0 ; -25 \Big\} \\ -----------------\)
2. \(-6x^2+0x=0 \\ \Leftrightarrow -6x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-6} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(6x^2-14x=0 \\ \Leftrightarrow x(6x-14) = 0 \\ \Leftrightarrow x = 0 \vee 6x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{6} = \frac{7}{3} \\ V = \Big\{ \frac{7}{3}; 0 \Big\} \\ -----------------\)
4. \(2x^2+7x=4x^2+9x \\ \Leftrightarrow -2x^2-2x=0 \\ \Leftrightarrow x(-2x-2) = 0 \\ \Leftrightarrow x = 0 \vee -2x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-2} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
5. \(-7x^2-20x=0 \\ \Leftrightarrow x(-7x-20) = 0 \\ \Leftrightarrow x = 0 \vee -7x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-7} = \frac{-20}{7} \\ V = \Big\{ 0 ; \frac{-20}{7} \Big\} \\ -----------------\)
6. \(6x^2-1x=0 \\ \Leftrightarrow x(6x-1) = 0 \\ \Leftrightarrow x = 0 \vee 6x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{6} \\ V = \Big\{ \frac{1}{6}; 0 \Big\} \\ -----------------\)
7. \(3(8x^2+5x)=-(-31x^2-31x) \\ \Leftrightarrow 24x^2+15x=31x^2+31x \\ \Leftrightarrow 24x^2+15x-31x^2-31x= 0 \\ \Leftrightarrow -7x^2+16x=0 \\ \Leftrightarrow x(-7x+16) = 0 \\ \Leftrightarrow x = 0 \vee -7x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-7} = \frac{16}{7} \\ V = \Big\{ \frac{16}{7}; 0 \Big\} \\ -----------------\)
8. \(-2x^2+5x=0 \\ \Leftrightarrow x(-2x+5) = 0 \\ \Leftrightarrow x = 0 \vee -2x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-2} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
9. \(10x^2+8x=8x^2-7x \\ \Leftrightarrow 2x^2+15x=0 \\ \Leftrightarrow x(2x+15) = 0 \\ \Leftrightarrow x = 0 \vee 2x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{2} \\ V = \Big\{ 0 ; \frac{-15}{2} \Big\} \\ -----------------\)
10. \(-8x^2-6x=-2x^2-5x \\ \Leftrightarrow -6x^2-1x=0 \\ \Leftrightarrow x(-6x-1) = 0 \\ \Leftrightarrow x = 0 \vee -6x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-6} = \frac{-1}{6} \\ V = \Big\{ 0 ; \frac{-1}{6} \Big\} \\ -----------------\)
11. \(10x^2+13x=4x^2+8x \\ \Leftrightarrow 6x^2+5x=0 \\ \Leftrightarrow x(6x+5) = 0 \\ \Leftrightarrow x = 0 \vee 6x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{6} \\ V = \Big\{ 0 ; \frac{-5}{6} \Big\} \\ -----------------\)
12. \(-3(8x^2+2x)=-(21x^2+13x) \\ \Leftrightarrow -24x^2-6x=-21x^2-13x \\ \Leftrightarrow -24x^2-6x+21x^2+13x= 0 \\ \Leftrightarrow -3x^2-7x=0 \\ \Leftrightarrow x(-3x-7) = 0 \\ \Leftrightarrow x = 0 \vee -3x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-3} = \frac{-7}{3} \\ V = \Big\{ 0 ; \frac{-7}{3} \Big\} \\ -----------------\)