Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-7x^2-3x=0\)
2. \(6x^2+25x=0\)
3. \(5(-8x^2-7x)=-(36x^2+44x)\)
4. \(x^2+19x=0\)
5. \(-4x^2+7x=0\)
6. \(3(8x^2-7x)=-(-26x^2+18x)\)
7. \(-3x^2-16x=-9x^2-3x\)
8. \(3x^2+7x=0\)
9. \(11x^2+18x=4x^2-6x\)
10. \(2(-9x^2-9x)=-(13x^2+5x)\)
11. \(2x^2+5x=0\)
12. \(-11x^2+11x=-3x^2+4x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-7x^2-3x=0 \\ \Leftrightarrow x(-7x-3) = 0 \\ \Leftrightarrow x = 0 \vee -7x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-7} = \frac{-3}{7} \\ V = \Big\{ 0 ; \frac{-3}{7} \Big\} \\ -----------------\)
2. \(6x^2+25x=0 \\ \Leftrightarrow x(6x+25) = 0 \\ \Leftrightarrow x = 0 \vee 6x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{6} \\ V = \Big\{ 0 ; \frac{-25}{6} \Big\} \\ -----------------\)
3. \(5(-8x^2-7x)=-(36x^2+44x) \\ \Leftrightarrow -40x^2-35x=-36x^2-44x \\ \Leftrightarrow -40x^2-35x+36x^2+44x= 0 \\ \Leftrightarrow -4x^2-9x=0 \\ \Leftrightarrow x(-4x-9) = 0 \\ \Leftrightarrow x = 0 \vee -4x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-4} = \frac{-9}{4} \\ V = \Big\{ 0 ; \frac{-9}{4} \Big\} \\ -----------------\)
4. \(x^2+19x=0 \\ \Leftrightarrow x(x+19) = 0 \\ \Leftrightarrow x = 0 \vee x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{1} = -19 \\ V = \Big\{ 0 ; -19 \Big\} \\ -----------------\)
5. \(-4x^2+7x=0 \\ \Leftrightarrow x(-4x+7) = 0 \\ \Leftrightarrow x = 0 \vee -4x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-4} = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)
6. \(3(8x^2-7x)=-(-26x^2+18x) \\ \Leftrightarrow 24x^2-21x=26x^2-18x \\ \Leftrightarrow 24x^2-21x-26x^2+18x= 0 \\ \Leftrightarrow -2x^2+3x=0 \\ \Leftrightarrow x(-2x+3) = 0 \\ \Leftrightarrow x = 0 \vee -2x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-2} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
7. \(-3x^2-16x=-9x^2-3x \\ \Leftrightarrow 6x^2-13x=0 \\ \Leftrightarrow x(6x-13) = 0 \\ \Leftrightarrow x = 0 \vee 6x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{6} \\ V = \Big\{ \frac{13}{6}; 0 \Big\} \\ -----------------\)
8. \(3x^2+7x=0 \\ \Leftrightarrow x(3x+7) = 0 \\ \Leftrightarrow x = 0 \vee 3x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{3} \\ V = \Big\{ 0 ; \frac{-7}{3} \Big\} \\ -----------------\)
9. \(11x^2+18x=4x^2-6x \\ \Leftrightarrow 7x^2+24x=0 \\ \Leftrightarrow x(7x+24) = 0 \\ \Leftrightarrow x = 0 \vee 7x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{7} \\ V = \Big\{ 0 ; \frac{-24}{7} \Big\} \\ -----------------\)
10. \(2(-9x^2-9x)=-(13x^2+5x) \\ \Leftrightarrow -18x^2-18x=-13x^2-5x \\ \Leftrightarrow -18x^2-18x+13x^2+5x= 0 \\ \Leftrightarrow -5x^2+13x=0 \\ \Leftrightarrow x(-5x+13) = 0 \\ \Leftrightarrow x = 0 \vee -5x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-5} = \frac{13}{5} \\ V = \Big\{ \frac{13}{5}; 0 \Big\} \\ -----------------\)
11. \(2x^2+5x=0 \\ \Leftrightarrow x(2x+5) = 0 \\ \Leftrightarrow x = 0 \vee 2x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
12. \(-11x^2+11x=-3x^2+4x \\ \Leftrightarrow -8x^2+7x=0 \\ \Leftrightarrow x(-8x+7) = 0 \\ \Leftrightarrow x = 0 \vee -8x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-8} = \frac{7}{8} \\ V = \Big\{ \frac{7}{8}; 0 \Big\} \\ -----------------\)