Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2-20x=0\)
2. \(15x^2-7x=8x^2+9x\)
3. \(-10x^2+7x=-6x^2-4x\)
4. \(-9x^2+18x=-8x^2-5x\)
5. \(4(-7x^2+8x)=-(26x^2-54x)\)
6. \(7x^2-19x=0\)
7. \(-15x^2-23x=-9x^2-3x\)
8. \(6x^2-11x=0\)
9. \(-x^2+24x=4x^2+9x\)
10. \(-6x^2-5x=0\)
11. \(-10x^2+20x=-4x^2+3x\)
12. \(-2x^2-8x=5x^2-3x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2-20x=0 \\ \Leftrightarrow x(4x-20) = 0 \\ \Leftrightarrow x = 0 \vee 4x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{4} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
2. \(15x^2-7x=8x^2+9x \\ \Leftrightarrow 7x^2-16x=0 \\ \Leftrightarrow x(7x-16) = 0 \\ \Leftrightarrow x = 0 \vee 7x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{7} \\ V = \Big\{ \frac{16}{7}; 0 \Big\} \\ -----------------\)
3. \(-10x^2+7x=-6x^2-4x \\ \Leftrightarrow -4x^2+11x=0 \\ \Leftrightarrow x(-4x+11) = 0 \\ \Leftrightarrow x = 0 \vee -4x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-4} = \frac{11}{4} \\ V = \Big\{ \frac{11}{4}; 0 \Big\} \\ -----------------\)
4. \(-9x^2+18x=-8x^2-5x \\ \Leftrightarrow -x^2+23x=0 \\ \Leftrightarrow x(-x+23) = 0 \\ \Leftrightarrow x = 0 \vee -x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-1} = 23 \\ V = \Big\{ 23; 0 \Big\} \\ -----------------\)
5. \(4(-7x^2+8x)=-(26x^2-54x) \\ \Leftrightarrow -28x^2+32x=-26x^2+54x \\ \Leftrightarrow -28x^2+32x+26x^2-54x= 0 \\ \Leftrightarrow -2x^2+22x=0 \\ \Leftrightarrow x(-2x+22) = 0 \\ \Leftrightarrow x = 0 \vee -2x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-2} = 11 \\ V = \Big\{ 11; 0 \Big\} \\ -----------------\)
6. \(7x^2-19x=0 \\ \Leftrightarrow x(7x-19) = 0 \\ \Leftrightarrow x = 0 \vee 7x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{7} \\ V = \Big\{ \frac{19}{7}; 0 \Big\} \\ -----------------\)
7. \(-15x^2-23x=-9x^2-3x \\ \Leftrightarrow -6x^2-20x=0 \\ \Leftrightarrow x(-6x-20) = 0 \\ \Leftrightarrow x = 0 \vee -6x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-6} = \frac{-10}{3} \\ V = \Big\{ 0 ; \frac{-10}{3} \Big\} \\ -----------------\)
8. \(6x^2-11x=0 \\ \Leftrightarrow x(6x-11) = 0 \\ \Leftrightarrow x = 0 \vee 6x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{6} \\ V = \Big\{ \frac{11}{6}; 0 \Big\} \\ -----------------\)
9. \(-x^2+24x=4x^2+9x \\ \Leftrightarrow -5x^2+15x=0 \\ \Leftrightarrow x(-5x+15) = 0 \\ \Leftrightarrow x = 0 \vee -5x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-5} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
10. \(-6x^2-5x=0 \\ \Leftrightarrow x(-6x-5) = 0 \\ \Leftrightarrow x = 0 \vee -6x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-6} = \frac{-5}{6} \\ V = \Big\{ 0 ; \frac{-5}{6} \Big\} \\ -----------------\)
11. \(-10x^2+20x=-4x^2+3x \\ \Leftrightarrow -6x^2+17x=0 \\ \Leftrightarrow x(-6x+17) = 0 \\ \Leftrightarrow x = 0 \vee -6x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-6} = \frac{17}{6} \\ V = \Big\{ \frac{17}{6}; 0 \Big\} \\ -----------------\)
12. \(-2x^2-8x=5x^2-3x \\ \Leftrightarrow -7x^2-5x=0 \\ \Leftrightarrow x(-7x-5) = 0 \\ \Leftrightarrow x = 0 \vee -7x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-7} = \frac{-5}{7} \\ V = \Big\{ 0 ; \frac{-5}{7} \Big\} \\ -----------------\)