Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(-3x^2+7x)=-(9x^2-10x)\)
2. \(14x^2-27x=9x^2-3x\)
3. \(-3(5x^2+10x)=-(17x^2+21x)\)
4. \(-4(4x^2+8x)=-(21x^2+12x)\)
5. \(-4(-3x^2-8x)=-(-8x^2-39x)\)
6. \(-2x^2-18x=0\)
7. \(-11x^2-28x=-9x^2-3x\)
8. \(5(3x^2+4x)=-(-23x^2-22x)\)
9. \(-7x^2-23x=0\)
10. \(-4(4x^2-3x)=-(23x^2-29x)\)
11. \(11x^2+9x=5x^2-4x\)
12. \(-3x^2+7x=2x^2-10x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(-3x^2+7x)=-(9x^2-10x) \\ \Leftrightarrow -15x^2+35x=-9x^2+10x \\ \Leftrightarrow -15x^2+35x+9x^2-10x= 0 \\ \Leftrightarrow -6x^2-25x=0 \\ \Leftrightarrow x(-6x-25) = 0 \\ \Leftrightarrow x = 0 \vee -6x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-6} = \frac{-25}{6} \\ V = \Big\{ 0 ; \frac{-25}{6} \Big\} \\ -----------------\)
2. \(14x^2-27x=9x^2-3x \\ \Leftrightarrow 5x^2-24x=0 \\ \Leftrightarrow x(5x-24) = 0 \\ \Leftrightarrow x = 0 \vee 5x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{5} \\ V = \Big\{ \frac{24}{5}; 0 \Big\} \\ -----------------\)
3. \(-3(5x^2+10x)=-(17x^2+21x) \\ \Leftrightarrow -15x^2-30x=-17x^2-21x \\ \Leftrightarrow -15x^2-30x+17x^2+21x= 0 \\ \Leftrightarrow 2x^2+9x=0 \\ \Leftrightarrow x(2x+9) = 0 \\ \Leftrightarrow x = 0 \vee 2x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{2} \\ V = \Big\{ 0 ; \frac{-9}{2} \Big\} \\ -----------------\)
4. \(-4(4x^2+8x)=-(21x^2+12x) \\ \Leftrightarrow -16x^2-32x=-21x^2-12x \\ \Leftrightarrow -16x^2-32x+21x^2+12x= 0 \\ \Leftrightarrow 5x^2+20x=0 \\ \Leftrightarrow x(5x+20) = 0 \\ \Leftrightarrow x = 0 \vee 5x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{5} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
5. \(-4(-3x^2-8x)=-(-8x^2-39x) \\ \Leftrightarrow 12x^2+32x=8x^2+39x \\ \Leftrightarrow 12x^2+32x-8x^2-39x= 0 \\ \Leftrightarrow 4x^2+7x=0 \\ \Leftrightarrow x(4x+7) = 0 \\ \Leftrightarrow x = 0 \vee 4x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)
6. \(-2x^2-18x=0 \\ \Leftrightarrow x(-2x-18) = 0 \\ \Leftrightarrow x = 0 \vee -2x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-2} = -9 \\ V = \Big\{ 0 ; -9 \Big\} \\ -----------------\)
7. \(-11x^2-28x=-9x^2-3x \\ \Leftrightarrow -2x^2-25x=0 \\ \Leftrightarrow x(-2x-25) = 0 \\ \Leftrightarrow x = 0 \vee -2x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-2} = \frac{-25}{2} \\ V = \Big\{ 0 ; \frac{-25}{2} \Big\} \\ -----------------\)
8. \(5(3x^2+4x)=-(-23x^2-22x) \\ \Leftrightarrow 15x^2+20x=23x^2+22x \\ \Leftrightarrow 15x^2+20x-23x^2-22x= 0 \\ \Leftrightarrow -8x^2+2x=0 \\ \Leftrightarrow x(-8x+2) = 0 \\ \Leftrightarrow x = 0 \vee -8x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-8} = \frac{1}{4} \\ V = \Big\{ \frac{1}{4}; 0 \Big\} \\ -----------------\)
9. \(-7x^2-23x=0 \\ \Leftrightarrow x(-7x-23) = 0 \\ \Leftrightarrow x = 0 \vee -7x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-7} = \frac{-23}{7} \\ V = \Big\{ 0 ; \frac{-23}{7} \Big\} \\ -----------------\)
10. \(-4(4x^2-3x)=-(23x^2-29x) \\ \Leftrightarrow -16x^2+12x=-23x^2+29x \\ \Leftrightarrow -16x^2+12x+23x^2-29x= 0 \\ \Leftrightarrow 7x^2+17x=0 \\ \Leftrightarrow x(7x+17) = 0 \\ \Leftrightarrow x = 0 \vee 7x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{7} \\ V = \Big\{ 0 ; \frac{-17}{7} \Big\} \\ -----------------\)
11. \(11x^2+9x=5x^2-4x \\ \Leftrightarrow 6x^2+13x=0 \\ \Leftrightarrow x(6x+13) = 0 \\ \Leftrightarrow x = 0 \vee 6x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{6} \\ V = \Big\{ 0 ; \frac{-13}{6} \Big\} \\ -----------------\)
12. \(-3x^2+7x=2x^2-10x \\ \Leftrightarrow -5x^2+17x=0 \\ \Leftrightarrow x(-5x+17) = 0 \\ \Leftrightarrow x = 0 \vee -5x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-5} = \frac{17}{5} \\ V = \Big\{ \frac{17}{5}; 0 \Big\} \\ -----------------\)