Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2-5x=0\)
2. \(5x^2-13x=10x^2-3x\)
3. \(-4(-5x^2+10x)=-(-28x^2+59x)\)
4. \(-4(-9x^2-7x)=-(-30x^2-29x)\)
5. \(6x^2-19x=0\)
6. \(-x^2-19x=5x^2-7x\)
7. \(-5x^2-18x=0\)
8. \(8x^2-13x=2x^2-9x\)
9. \(10x^2+27x=7x^2+2x\)
10. \(-8x^2+16x=-3x^2+2x\)
11. \(2x^2+15x=0\)
12. \(-2(-2x^2-6x)=-(-9x^2+x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2-5x=0 \\ \Leftrightarrow x(-8x-5) = 0 \\ \Leftrightarrow x = 0 \vee -8x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-8} = \frac{-5}{8} \\ V = \Big\{ 0 ; \frac{-5}{8} \Big\} \\ -----------------\)
2. \(5x^2-13x=10x^2-3x \\ \Leftrightarrow -5x^2-10x=0 \\ \Leftrightarrow x(-5x-10) = 0 \\ \Leftrightarrow x = 0 \vee -5x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-5} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
3. \(-4(-5x^2+10x)=-(-28x^2+59x) \\ \Leftrightarrow 20x^2-40x=28x^2-59x \\ \Leftrightarrow 20x^2-40x-28x^2+59x= 0 \\ \Leftrightarrow -8x^2-19x=0 \\ \Leftrightarrow x(-8x-19) = 0 \\ \Leftrightarrow x = 0 \vee -8x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-8} = \frac{-19}{8} \\ V = \Big\{ 0 ; \frac{-19}{8} \Big\} \\ -----------------\)
4. \(-4(-9x^2-7x)=-(-30x^2-29x) \\ \Leftrightarrow 36x^2+28x=30x^2+29x \\ \Leftrightarrow 36x^2+28x-30x^2-29x= 0 \\ \Leftrightarrow 6x^2+1x=0 \\ \Leftrightarrow x(6x+1) = 0 \\ \Leftrightarrow x = 0 \vee 6x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{6} \\ V = \Big\{ 0 ; \frac{-1}{6} \Big\} \\ -----------------\)
5. \(6x^2-19x=0 \\ \Leftrightarrow x(6x-19) = 0 \\ \Leftrightarrow x = 0 \vee 6x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{6} \\ V = \Big\{ \frac{19}{6}; 0 \Big\} \\ -----------------\)
6. \(-x^2-19x=5x^2-7x \\ \Leftrightarrow -6x^2-12x=0 \\ \Leftrightarrow x(-6x-12) = 0 \\ \Leftrightarrow x = 0 \vee -6x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-6} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
7. \(-5x^2-18x=0 \\ \Leftrightarrow x(-5x-18) = 0 \\ \Leftrightarrow x = 0 \vee -5x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-5} = \frac{-18}{5} \\ V = \Big\{ 0 ; \frac{-18}{5} \Big\} \\ -----------------\)
8. \(8x^2-13x=2x^2-9x \\ \Leftrightarrow 6x^2-4x=0 \\ \Leftrightarrow x(6x-4) = 0 \\ \Leftrightarrow x = 0 \vee 6x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{6} = \frac{2}{3} \\ V = \Big\{ \frac{2}{3}; 0 \Big\} \\ -----------------\)
9. \(10x^2+27x=7x^2+2x \\ \Leftrightarrow 3x^2+25x=0 \\ \Leftrightarrow x(3x+25) = 0 \\ \Leftrightarrow x = 0 \vee 3x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{3} \\ V = \Big\{ 0 ; \frac{-25}{3} \Big\} \\ -----------------\)
10. \(-8x^2+16x=-3x^2+2x \\ \Leftrightarrow -5x^2+14x=0 \\ \Leftrightarrow x(-5x+14) = 0 \\ \Leftrightarrow x = 0 \vee -5x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-5} = \frac{14}{5} \\ V = \Big\{ \frac{14}{5}; 0 \Big\} \\ -----------------\)
11. \(2x^2+15x=0 \\ \Leftrightarrow x(2x+15) = 0 \\ \Leftrightarrow x = 0 \vee 2x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{2} \\ V = \Big\{ 0 ; \frac{-15}{2} \Big\} \\ -----------------\)
12. \(-2(-2x^2-6x)=-(-9x^2+x) \\ \Leftrightarrow 4x^2+12x=9x^2-x \\ \Leftrightarrow 4x^2+12x-9x^2+x= 0 \\ \Leftrightarrow -5x^2-13x=0 \\ \Leftrightarrow x(-5x-13) = 0 \\ \Leftrightarrow x = 0 \vee -5x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-5} = \frac{-13}{5} \\ V = \Big\{ 0 ; \frac{-13}{5} \Big\} \\ -----------------\)