Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2-3x=0\)
2. \(-x^2-9x=-4x^2+9x\)
3. \(-6x^2+7x=2x^2+2x\)
4. \(2(3x^2+3x)=-(-2x^2+11x)\)
5. \(3x^2-20x=0\)
6. \(-6x^2-2x=0\)
7. \(10x^2-x=8x^2-6x\)
8. \(-5(-6x^2-10x)=-(-35x^2-42x)\)
9. \(-3(-10x^2-8x)=-(-37x^2-23x)\)
10. \(4(-5x^2-10x)=-(13x^2+42x)\)
11. \(-4x^2+10x=0\)
12. \(3(2x^2-8x)=-(-7x^2+8x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2-3x=0 \\ \Leftrightarrow x(-4x-3) = 0 \\ \Leftrightarrow x = 0 \vee -4x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-4} = \frac{-3}{4} \\ V = \Big\{ 0 ; \frac{-3}{4} \Big\} \\ -----------------\)
2. \(-x^2-9x=-4x^2+9x \\ \Leftrightarrow 3x^2-18x=0 \\ \Leftrightarrow x(3x-18) = 0 \\ \Leftrightarrow x = 0 \vee 3x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{3} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
3. \(-6x^2+7x=2x^2+2x \\ \Leftrightarrow -8x^2+5x=0 \\ \Leftrightarrow x(-8x+5) = 0 \\ \Leftrightarrow x = 0 \vee -8x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-8} = \frac{5}{8} \\ V = \Big\{ \frac{5}{8}; 0 \Big\} \\ -----------------\)
4. \(2(3x^2+3x)=-(-2x^2+11x) \\ \Leftrightarrow 6x^2+6x=2x^2-11x \\ \Leftrightarrow 6x^2+6x-2x^2+11x= 0 \\ \Leftrightarrow 4x^2-17x=0 \\ \Leftrightarrow x(4x-17) = 0 \\ \Leftrightarrow x = 0 \vee 4x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{4} \\ V = \Big\{ \frac{17}{4}; 0 \Big\} \\ -----------------\)
5. \(3x^2-20x=0 \\ \Leftrightarrow x(3x-20) = 0 \\ \Leftrightarrow x = 0 \vee 3x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{3} \\ V = \Big\{ \frac{20}{3}; 0 \Big\} \\ -----------------\)
6. \(-6x^2-2x=0 \\ \Leftrightarrow x(-6x-2) = 0 \\ \Leftrightarrow x = 0 \vee -6x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-6} = \frac{-1}{3} \\ V = \Big\{ 0 ; \frac{-1}{3} \Big\} \\ -----------------\)
7. \(10x^2-x=8x^2-6x \\ \Leftrightarrow 2x^2+5x=0 \\ \Leftrightarrow x(2x+5) = 0 \\ \Leftrightarrow x = 0 \vee 2x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
8. \(-5(-6x^2-10x)=-(-35x^2-42x) \\ \Leftrightarrow 30x^2+50x=35x^2+42x \\ \Leftrightarrow 30x^2+50x-35x^2-42x= 0 \\ \Leftrightarrow -5x^2-8x=0 \\ \Leftrightarrow x(-5x-8) = 0 \\ \Leftrightarrow x = 0 \vee -5x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-5} = \frac{-8}{5} \\ V = \Big\{ 0 ; \frac{-8}{5} \Big\} \\ -----------------\)
9. \(-3(-10x^2-8x)=-(-37x^2-23x) \\ \Leftrightarrow 30x^2+24x=37x^2+23x \\ \Leftrightarrow 30x^2+24x-37x^2-23x= 0 \\ \Leftrightarrow -7x^2-1x=0 \\ \Leftrightarrow x(-7x-1) = 0 \\ \Leftrightarrow x = 0 \vee -7x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-7} = \frac{-1}{7} \\ V = \Big\{ 0 ; \frac{-1}{7} \Big\} \\ -----------------\)
10. \(4(-5x^2-10x)=-(13x^2+42x) \\ \Leftrightarrow -20x^2-40x=-13x^2-42x \\ \Leftrightarrow -20x^2-40x+13x^2+42x= 0 \\ \Leftrightarrow -7x^2-2x=0 \\ \Leftrightarrow x(-7x-2) = 0 \\ \Leftrightarrow x = 0 \vee -7x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-7} = \frac{-2}{7} \\ V = \Big\{ 0 ; \frac{-2}{7} \Big\} \\ -----------------\)
11. \(-4x^2+10x=0 \\ \Leftrightarrow x(-4x+10) = 0 \\ \Leftrightarrow x = 0 \vee -4x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-4} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
12. \(3(2x^2-8x)=-(-7x^2+8x) \\ \Leftrightarrow 6x^2-24x=7x^2-8x \\ \Leftrightarrow 6x^2-24x-7x^2+8x= 0 \\ \Leftrightarrow -x^2+16x=0 \\ \Leftrightarrow x(-x+16) = 0 \\ \Leftrightarrow x = 0 \vee -x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-1} = 16 \\ V = \Big\{ 16; 0 \Big\} \\ -----------------\)