Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(6x^2-10x)=-(-16x^2+53x)\)
2. \(4x^2+12x=0\)
3. \(-4x^2-16x=2x^2-7x\)
4. \(-3(-3x^2+9x)=-(-17x^2+42x)\)
5. \(-x^2-4x=-5x^2+2x\)
6. \(2(-4x^2-3x)=-(16x^2+13x)\)
7. \(-3(10x^2-7x)=-(36x^2-15x)\)
8. \(5(3x^2+7x)=-(-20x^2-48x)\)
9. \(-7x^2-12x=-3x^2+7x\)
10. \(9x^2-12x=5x^2+2x\)
11. \(7x^2+6x=4x^2-6x\)
12. \(-3(-5x^2-7x)=-(-8x^2-27x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(6x^2-10x)=-(-16x^2+53x) \\ \Leftrightarrow 24x^2-40x=16x^2-53x \\ \Leftrightarrow 24x^2-40x-16x^2+53x= 0 \\ \Leftrightarrow 8x^2-13x=0 \\ \Leftrightarrow x(8x-13) = 0 \\ \Leftrightarrow x = 0 \vee 8x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{8} \\ V = \Big\{ \frac{13}{8}; 0 \Big\} \\ -----------------\)
2. \(4x^2+12x=0 \\ \Leftrightarrow x(4x+12) = 0 \\ \Leftrightarrow x = 0 \vee 4x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{4} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
3. \(-4x^2-16x=2x^2-7x \\ \Leftrightarrow -6x^2-9x=0 \\ \Leftrightarrow x(-6x-9) = 0 \\ \Leftrightarrow x = 0 \vee -6x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-6} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
4. \(-3(-3x^2+9x)=-(-17x^2+42x) \\ \Leftrightarrow 9x^2-27x=17x^2-42x \\ \Leftrightarrow 9x^2-27x-17x^2+42x= 0 \\ \Leftrightarrow -8x^2-15x=0 \\ \Leftrightarrow x(-8x-15) = 0 \\ \Leftrightarrow x = 0 \vee -8x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-8} = \frac{-15}{8} \\ V = \Big\{ 0 ; \frac{-15}{8} \Big\} \\ -----------------\)
5. \(-x^2-4x=-5x^2+2x \\ \Leftrightarrow 4x^2-6x=0 \\ \Leftrightarrow x(4x-6) = 0 \\ \Leftrightarrow x = 0 \vee 4x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{4} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
6. \(2(-4x^2-3x)=-(16x^2+13x) \\ \Leftrightarrow -8x^2-6x=-16x^2-13x \\ \Leftrightarrow -8x^2-6x+16x^2+13x= 0 \\ \Leftrightarrow 8x^2-7x=0 \\ \Leftrightarrow x(8x-7) = 0 \\ \Leftrightarrow x = 0 \vee 8x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{8} \\ V = \Big\{ \frac{7}{8}; 0 \Big\} \\ -----------------\)
7. \(-3(10x^2-7x)=-(36x^2-15x) \\ \Leftrightarrow -30x^2+21x=-36x^2+15x \\ \Leftrightarrow -30x^2+21x+36x^2-15x= 0 \\ \Leftrightarrow 6x^2-6x=0 \\ \Leftrightarrow x(6x-6) = 0 \\ \Leftrightarrow x = 0 \vee 6x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{6} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
8. \(5(3x^2+7x)=-(-20x^2-48x) \\ \Leftrightarrow 15x^2+35x=20x^2+48x \\ \Leftrightarrow 15x^2+35x-20x^2-48x= 0 \\ \Leftrightarrow -5x^2+13x=0 \\ \Leftrightarrow x(-5x+13) = 0 \\ \Leftrightarrow x = 0 \vee -5x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-5} = \frac{13}{5} \\ V = \Big\{ \frac{13}{5}; 0 \Big\} \\ -----------------\)
9. \(-7x^2-12x=-3x^2+7x \\ \Leftrightarrow -4x^2-19x=0 \\ \Leftrightarrow x(-4x-19) = 0 \\ \Leftrightarrow x = 0 \vee -4x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-4} = \frac{-19}{4} \\ V = \Big\{ 0 ; \frac{-19}{4} \Big\} \\ -----------------\)
10. \(9x^2-12x=5x^2+2x \\ \Leftrightarrow 4x^2-14x=0 \\ \Leftrightarrow x(4x-14) = 0 \\ \Leftrightarrow x = 0 \vee 4x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{4} = \frac{7}{2} \\ V = \Big\{ \frac{7}{2}; 0 \Big\} \\ -----------------\)
11. \(7x^2+6x=4x^2-6x \\ \Leftrightarrow 3x^2+12x=0 \\ \Leftrightarrow x(3x+12) = 0 \\ \Leftrightarrow x = 0 \vee 3x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{3} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
12. \(-3(-5x^2-7x)=-(-8x^2-27x) \\ \Leftrightarrow 15x^2+21x=8x^2+27x \\ \Leftrightarrow 15x^2+21x-8x^2-27x= 0 \\ \Leftrightarrow 7x^2+6x=0 \\ \Leftrightarrow x(7x+6) = 0 \\ \Leftrightarrow x = 0 \vee 7x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{7} \\ V = \Big\{ 0 ; \frac{-6}{7} \Big\} \\ -----------------\)