Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(-7x^2-8x)=-(29x^2+44x)\)
2. \(-5x^2+14x=0\)
3. \(4(5x^2-9x)=-(-14x^2+35x)\)
4. \(-x^2+11x=4x^2+10x\)
5. \(7x^2+11x=0\)
6. \(4(3x^2+10x)=-(-17x^2-56x)\)
7. \(2(10x^2-2x)=-(-26x^2-2x)\)
8. \(-8x^2-17x=-3x^2+2x\)
9. \(5x^2+4x=0\)
10. \(7x^2-27x=2x^2-5x\)
11. \(5x^2+10x=0\)
12. \(-7x^2+9x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(-7x^2-8x)=-(29x^2+44x) \\ \Leftrightarrow -28x^2-32x=-29x^2-44x \\ \Leftrightarrow -28x^2-32x+29x^2+44x= 0 \\ \Leftrightarrow x^2-12x=0 \\ \Leftrightarrow x(x-12) = 0 \\ \Leftrightarrow x = 0 \vee x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{1} = 12 \\ V = \Big\{ 12; 0 \Big\} \\ -----------------\)
2. \(-5x^2+14x=0 \\ \Leftrightarrow x(-5x+14) = 0 \\ \Leftrightarrow x = 0 \vee -5x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-5} = \frac{14}{5} \\ V = \Big\{ \frac{14}{5}; 0 \Big\} \\ -----------------\)
3. \(4(5x^2-9x)=-(-14x^2+35x) \\ \Leftrightarrow 20x^2-36x=14x^2-35x \\ \Leftrightarrow 20x^2-36x-14x^2+35x= 0 \\ \Leftrightarrow 6x^2+1x=0 \\ \Leftrightarrow x(6x+1) = 0 \\ \Leftrightarrow x = 0 \vee 6x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{6} \\ V = \Big\{ 0 ; \frac{-1}{6} \Big\} \\ -----------------\)
4. \(-x^2+11x=4x^2+10x \\ \Leftrightarrow -5x^2+1x=0 \\ \Leftrightarrow x(-5x+1) = 0 \\ \Leftrightarrow x = 0 \vee -5x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-5} = \frac{1}{5} \\ V = \Big\{ \frac{1}{5}; 0 \Big\} \\ -----------------\)
5. \(7x^2+11x=0 \\ \Leftrightarrow x(7x+11) = 0 \\ \Leftrightarrow x = 0 \vee 7x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{7} \\ V = \Big\{ 0 ; \frac{-11}{7} \Big\} \\ -----------------\)
6. \(4(3x^2+10x)=-(-17x^2-56x) \\ \Leftrightarrow 12x^2+40x=17x^2+56x \\ \Leftrightarrow 12x^2+40x-17x^2-56x= 0 \\ \Leftrightarrow -5x^2+16x=0 \\ \Leftrightarrow x(-5x+16) = 0 \\ \Leftrightarrow x = 0 \vee -5x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-5} = \frac{16}{5} \\ V = \Big\{ \frac{16}{5}; 0 \Big\} \\ -----------------\)
7. \(2(10x^2-2x)=-(-26x^2-2x) \\ \Leftrightarrow 20x^2-4x=26x^2+2x \\ \Leftrightarrow 20x^2-4x-26x^2-2x= 0 \\ \Leftrightarrow -6x^2+6x=0 \\ \Leftrightarrow x(-6x+6) = 0 \\ \Leftrightarrow x = 0 \vee -6x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-6} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
8. \(-8x^2-17x=-3x^2+2x \\ \Leftrightarrow -5x^2-19x=0 \\ \Leftrightarrow x(-5x-19) = 0 \\ \Leftrightarrow x = 0 \vee -5x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-5} = \frac{-19}{5} \\ V = \Big\{ 0 ; \frac{-19}{5} \Big\} \\ -----------------\)
9. \(5x^2+4x=0 \\ \Leftrightarrow x(5x+4) = 0 \\ \Leftrightarrow x = 0 \vee 5x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{5} \\ V = \Big\{ 0 ; \frac{-4}{5} \Big\} \\ -----------------\)
10. \(7x^2-27x=2x^2-5x \\ \Leftrightarrow 5x^2-22x=0 \\ \Leftrightarrow x(5x-22) = 0 \\ \Leftrightarrow x = 0 \vee 5x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{5} \\ V = \Big\{ \frac{22}{5}; 0 \Big\} \\ -----------------\)
11. \(5x^2+10x=0 \\ \Leftrightarrow x(5x+10) = 0 \\ \Leftrightarrow x = 0 \vee 5x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{5} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
12. \(-7x^2+9x=0 \\ \Leftrightarrow x(-7x+9) = 0 \\ \Leftrightarrow x = 0 \vee -7x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-7} = \frac{9}{7} \\ V = \Big\{ \frac{9}{7}; 0 \Big\} \\ -----------------\)