Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-7x^2+21x=-10x^2+4x\)
2. \(-2(2x^2+8x)=-(-4x^2+37x)\)
3. \(-8x^2+20x=0\)
4. \(-3(-4x^2+7x)=-(-13x^2+44x)\)
5. \(4x^2-16x=10x^2-9x\)
6. \(x^2-11x=2x^2+4x\)
7. \(4x^2-9x=0\)
8. \(8x^2-5x=0\)
9. \(4(-5x^2+7x)=-(17x^2-7x)\)
10. \(3(-2x^2+9x)=-(2x^2-46x)\)
11. \(3x^2-14x=9x^2+7x\)
12. \(7x^2-22x=3x^2-5x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-7x^2+21x=-10x^2+4x \\ \Leftrightarrow 3x^2+17x=0 \\ \Leftrightarrow x(3x+17) = 0 \\ \Leftrightarrow x = 0 \vee 3x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{3} \\ V = \Big\{ 0 ; \frac{-17}{3} \Big\} \\ -----------------\)
2. \(-2(2x^2+8x)=-(-4x^2+37x) \\ \Leftrightarrow -4x^2-16x=4x^2-37x \\ \Leftrightarrow -4x^2-16x-4x^2+37x= 0 \\ \Leftrightarrow -8x^2-21x=0 \\ \Leftrightarrow x(-8x-21) = 0 \\ \Leftrightarrow x = 0 \vee -8x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-8} = \frac{-21}{8} \\ V = \Big\{ 0 ; \frac{-21}{8} \Big\} \\ -----------------\)
3. \(-8x^2+20x=0 \\ \Leftrightarrow x(-8x+20) = 0 \\ \Leftrightarrow x = 0 \vee -8x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-8} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
4. \(-3(-4x^2+7x)=-(-13x^2+44x) \\ \Leftrightarrow 12x^2-21x=13x^2-44x \\ \Leftrightarrow 12x^2-21x-13x^2+44x= 0 \\ \Leftrightarrow -x^2-23x=0 \\ \Leftrightarrow x(-x-23) = 0 \\ \Leftrightarrow x = 0 \vee -x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-1} = -23 \\ V = \Big\{ 0 ; -23 \Big\} \\ -----------------\)
5. \(4x^2-16x=10x^2-9x \\ \Leftrightarrow -6x^2-7x=0 \\ \Leftrightarrow x(-6x-7) = 0 \\ \Leftrightarrow x = 0 \vee -6x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-6} = \frac{-7}{6} \\ V = \Big\{ 0 ; \frac{-7}{6} \Big\} \\ -----------------\)
6. \(x^2-11x=2x^2+4x \\ \Leftrightarrow -x^2-15x=0 \\ \Leftrightarrow x(-x-15) = 0 \\ \Leftrightarrow x = 0 \vee -x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-1} = -15 \\ V = \Big\{ 0 ; -15 \Big\} \\ -----------------\)
7. \(4x^2-9x=0 \\ \Leftrightarrow x(4x-9) = 0 \\ \Leftrightarrow x = 0 \vee 4x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
8. \(8x^2-5x=0 \\ \Leftrightarrow x(8x-5) = 0 \\ \Leftrightarrow x = 0 \vee 8x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{8} \\ V = \Big\{ \frac{5}{8}; 0 \Big\} \\ -----------------\)
9. \(4(-5x^2+7x)=-(17x^2-7x) \\ \Leftrightarrow -20x^2+28x=-17x^2+7x \\ \Leftrightarrow -20x^2+28x+17x^2-7x= 0 \\ \Leftrightarrow -3x^2-21x=0 \\ \Leftrightarrow x(-3x-21) = 0 \\ \Leftrightarrow x = 0 \vee -3x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-3} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)
10. \(3(-2x^2+9x)=-(2x^2-46x) \\ \Leftrightarrow -6x^2+27x=-2x^2+46x \\ \Leftrightarrow -6x^2+27x+2x^2-46x= 0 \\ \Leftrightarrow -4x^2+19x=0 \\ \Leftrightarrow x(-4x+19) = 0 \\ \Leftrightarrow x = 0 \vee -4x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-4} = \frac{19}{4} \\ V = \Big\{ \frac{19}{4}; 0 \Big\} \\ -----------------\)
11. \(3x^2-14x=9x^2+7x \\ \Leftrightarrow -6x^2-21x=0 \\ \Leftrightarrow x(-6x-21) = 0 \\ \Leftrightarrow x = 0 \vee -6x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-6} = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)
12. \(7x^2-22x=3x^2-5x \\ \Leftrightarrow 4x^2-17x=0 \\ \Leftrightarrow x(4x-17) = 0 \\ \Leftrightarrow x = 0 \vee 4x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{4} \\ V = \Big\{ \frac{17}{4}; 0 \Big\} \\ -----------------\)