Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2-7x=0\)
2. \(-3x^2-13x=0\)
3. \(-2x^2+4x=-9x^2-2x\)
4. \(4x^2-19x=8x^2-7x\)
5. \(3x^2+16x=0\)
6. \(8x^2-1x=0\)
7. \(5x^2+24x=0\)
8. \(x^2-11x=0\)
9. \(3(-2x^2+7x)=-(-x^2-37x)\)
10. \(-x^2-33x=5x^2-10x\)
11. \(5x^2+5x=0\)
12. \(7x^2+16x=3x^2+2x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2-7x=0 \\ \Leftrightarrow x(3x-7) = 0 \\ \Leftrightarrow x = 0 \vee 3x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{3} \\ V = \Big\{ \frac{7}{3}; 0 \Big\} \\ -----------------\)
2. \(-3x^2-13x=0 \\ \Leftrightarrow x(-3x-13) = 0 \\ \Leftrightarrow x = 0 \vee -3x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-3} = \frac{-13}{3} \\ V = \Big\{ 0 ; \frac{-13}{3} \Big\} \\ -----------------\)
3. \(-2x^2+4x=-9x^2-2x \\ \Leftrightarrow 7x^2+6x=0 \\ \Leftrightarrow x(7x+6) = 0 \\ \Leftrightarrow x = 0 \vee 7x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{7} \\ V = \Big\{ 0 ; \frac{-6}{7} \Big\} \\ -----------------\)
4. \(4x^2-19x=8x^2-7x \\ \Leftrightarrow -4x^2-12x=0 \\ \Leftrightarrow x(-4x-12) = 0 \\ \Leftrightarrow x = 0 \vee -4x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-4} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
5. \(3x^2+16x=0 \\ \Leftrightarrow x(3x+16) = 0 \\ \Leftrightarrow x = 0 \vee 3x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{3} \\ V = \Big\{ 0 ; \frac{-16}{3} \Big\} \\ -----------------\)
6. \(8x^2-1x=0 \\ \Leftrightarrow x(8x-1) = 0 \\ \Leftrightarrow x = 0 \vee 8x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{8} \\ V = \Big\{ \frac{1}{8}; 0 \Big\} \\ -----------------\)
7. \(5x^2+24x=0 \\ \Leftrightarrow x(5x+24) = 0 \\ \Leftrightarrow x = 0 \vee 5x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{5} \\ V = \Big\{ 0 ; \frac{-24}{5} \Big\} \\ -----------------\)
8. \(x^2-11x=0 \\ \Leftrightarrow x(x-11) = 0 \\ \Leftrightarrow x = 0 \vee x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{1} = 11 \\ V = \Big\{ 11; 0 \Big\} \\ -----------------\)
9. \(3(-2x^2+7x)=-(-x^2-37x) \\ \Leftrightarrow -6x^2+21x=x^2+37x \\ \Leftrightarrow -6x^2+21x-x^2-37x= 0 \\ \Leftrightarrow -7x^2+16x=0 \\ \Leftrightarrow x(-7x+16) = 0 \\ \Leftrightarrow x = 0 \vee -7x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-7} = \frac{16}{7} \\ V = \Big\{ \frac{16}{7}; 0 \Big\} \\ -----------------\)
10. \(-x^2-33x=5x^2-10x \\ \Leftrightarrow -6x^2-23x=0 \\ \Leftrightarrow x(-6x-23) = 0 \\ \Leftrightarrow x = 0 \vee -6x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-6} = \frac{-23}{6} \\ V = \Big\{ 0 ; \frac{-23}{6} \Big\} \\ -----------------\)
11. \(5x^2+5x=0 \\ \Leftrightarrow x(5x+5) = 0 \\ \Leftrightarrow x = 0 \vee 5x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{5} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
12. \(7x^2+16x=3x^2+2x \\ \Leftrightarrow 4x^2+14x=0 \\ \Leftrightarrow x(4x+14) = 0 \\ \Leftrightarrow x = 0 \vee 4x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{4} = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)