Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2-20x=0\)
2. \(5x^2-18x=0\)
3. \(5(3x^2+10x)=-(-8x^2-45x)\)
4. \(-9x^2-11x=-10x^2-8x\)
5. \(14x^2+10x=9x^2+3x\)
6. \(-2(5x^2-7x)=-(4x^2-34x)\)
7. \(2x^2-9x=8x^2+4x\)
8. \(-6x^2+16x=0\)
9. \(-3x^2+11x=-4x^2+7x\)
10. \(5(-3x^2-8x)=-(20x^2+22x)\)
11. \(-14x^2+22x=-10x^2+4x\)
12. \(2x^2+7x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2-20x=0 \\ \Leftrightarrow x(7x-20) = 0 \\ \Leftrightarrow x = 0 \vee 7x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{7} \\ V = \Big\{ \frac{20}{7}; 0 \Big\} \\ -----------------\)
2. \(5x^2-18x=0 \\ \Leftrightarrow x(5x-18) = 0 \\ \Leftrightarrow x = 0 \vee 5x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{5} \\ V = \Big\{ \frac{18}{5}; 0 \Big\} \\ -----------------\)
3. \(5(3x^2+10x)=-(-8x^2-45x) \\ \Leftrightarrow 15x^2+50x=8x^2+45x \\ \Leftrightarrow 15x^2+50x-8x^2-45x= 0 \\ \Leftrightarrow 7x^2-5x=0 \\ \Leftrightarrow x(7x-5) = 0 \\ \Leftrightarrow x = 0 \vee 7x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{7} \\ V = \Big\{ \frac{5}{7}; 0 \Big\} \\ -----------------\)
4. \(-9x^2-11x=-10x^2-8x \\ \Leftrightarrow x^2-3x=0 \\ \Leftrightarrow x(x-3) = 0 \\ \Leftrightarrow x = 0 \vee x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{1} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
5. \(14x^2+10x=9x^2+3x \\ \Leftrightarrow 5x^2+7x=0 \\ \Leftrightarrow x(5x+7) = 0 \\ \Leftrightarrow x = 0 \vee 5x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{5} \\ V = \Big\{ 0 ; \frac{-7}{5} \Big\} \\ -----------------\)
6. \(-2(5x^2-7x)=-(4x^2-34x) \\ \Leftrightarrow -10x^2+14x=-4x^2+34x \\ \Leftrightarrow -10x^2+14x+4x^2-34x= 0 \\ \Leftrightarrow -6x^2+20x=0 \\ \Leftrightarrow x(-6x+20) = 0 \\ \Leftrightarrow x = 0 \vee -6x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-6} = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)
7. \(2x^2-9x=8x^2+4x \\ \Leftrightarrow -6x^2-13x=0 \\ \Leftrightarrow x(-6x-13) = 0 \\ \Leftrightarrow x = 0 \vee -6x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-6} = \frac{-13}{6} \\ V = \Big\{ 0 ; \frac{-13}{6} \Big\} \\ -----------------\)
8. \(-6x^2+16x=0 \\ \Leftrightarrow x(-6x+16) = 0 \\ \Leftrightarrow x = 0 \vee -6x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-6} = \frac{8}{3} \\ V = \Big\{ \frac{8}{3}; 0 \Big\} \\ -----------------\)
9. \(-3x^2+11x=-4x^2+7x \\ \Leftrightarrow x^2+4x=0 \\ \Leftrightarrow x(x+4) = 0 \\ \Leftrightarrow x = 0 \vee x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{1} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
10. \(5(-3x^2-8x)=-(20x^2+22x) \\ \Leftrightarrow -15x^2-40x=-20x^2-22x \\ \Leftrightarrow -15x^2-40x+20x^2+22x= 0 \\ \Leftrightarrow 5x^2+18x=0 \\ \Leftrightarrow x(5x+18) = 0 \\ \Leftrightarrow x = 0 \vee 5x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{5} \\ V = \Big\{ 0 ; \frac{-18}{5} \Big\} \\ -----------------\)
11. \(-14x^2+22x=-10x^2+4x \\ \Leftrightarrow -4x^2+18x=0 \\ \Leftrightarrow x(-4x+18) = 0 \\ \Leftrightarrow x = 0 \vee -4x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-4} = \frac{9}{2} \\ V = \Big\{ \frac{9}{2}; 0 \Big\} \\ -----------------\)
12. \(2x^2+7x=0 \\ \Leftrightarrow x(2x+7) = 0 \\ \Leftrightarrow x = 0 \vee 2x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)