Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2-7x=9x^2-4x\)
2. \(x^2-6x=0\)
3. \(-15x^2-8x=-10x^2+3x\)
4. \(-12x^2-28x=-5x^2-4x\)
5. \(-3(9x^2-10x)=-(34x^2-11x)\)
6. \(-2(-7x^2+8x)=-(-10x^2-8x)\)
7. \(10x^2+25x=4x^2+3x\)
8. \(-2x^2+19x=5x^2+6x\)
9. \(4x^2+1x=0\)
10. \(2(-6x^2+7x)=-(16x^2+10x)\)
11. \(-7x^2-17x=0\)
12. \(5x^2-4x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2-7x=9x^2-4x \\ \Leftrightarrow -6x^2-3x=0 \\ \Leftrightarrow x(-6x-3) = 0 \\ \Leftrightarrow x = 0 \vee -6x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-6} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
2. \(x^2-6x=0 \\ \Leftrightarrow x(x-6) = 0 \\ \Leftrightarrow x = 0 \vee x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{1} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
3. \(-15x^2-8x=-10x^2+3x \\ \Leftrightarrow -5x^2-11x=0 \\ \Leftrightarrow x(-5x-11) = 0 \\ \Leftrightarrow x = 0 \vee -5x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-5} = \frac{-11}{5} \\ V = \Big\{ 0 ; \frac{-11}{5} \Big\} \\ -----------------\)
4. \(-12x^2-28x=-5x^2-4x \\ \Leftrightarrow -7x^2-24x=0 \\ \Leftrightarrow x(-7x-24) = 0 \\ \Leftrightarrow x = 0 \vee -7x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-7} = \frac{-24}{7} \\ V = \Big\{ 0 ; \frac{-24}{7} \Big\} \\ -----------------\)
5. \(-3(9x^2-10x)=-(34x^2-11x) \\ \Leftrightarrow -27x^2+30x=-34x^2+11x \\ \Leftrightarrow -27x^2+30x+34x^2-11x= 0 \\ \Leftrightarrow 7x^2-19x=0 \\ \Leftrightarrow x(7x-19) = 0 \\ \Leftrightarrow x = 0 \vee 7x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{7} \\ V = \Big\{ \frac{19}{7}; 0 \Big\} \\ -----------------\)
6. \(-2(-7x^2+8x)=-(-10x^2-8x) \\ \Leftrightarrow 14x^2-16x=10x^2+8x \\ \Leftrightarrow 14x^2-16x-10x^2-8x= 0 \\ \Leftrightarrow 4x^2+24x=0 \\ \Leftrightarrow x(4x+24) = 0 \\ \Leftrightarrow x = 0 \vee 4x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{4} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
7. \(10x^2+25x=4x^2+3x \\ \Leftrightarrow 6x^2+22x=0 \\ \Leftrightarrow x(6x+22) = 0 \\ \Leftrightarrow x = 0 \vee 6x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{6} = \frac{-11}{3} \\ V = \Big\{ 0 ; \frac{-11}{3} \Big\} \\ -----------------\)
8. \(-2x^2+19x=5x^2+6x \\ \Leftrightarrow -7x^2+13x=0 \\ \Leftrightarrow x(-7x+13) = 0 \\ \Leftrightarrow x = 0 \vee -7x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-7} = \frac{13}{7} \\ V = \Big\{ \frac{13}{7}; 0 \Big\} \\ -----------------\)
9. \(4x^2+1x=0 \\ \Leftrightarrow x(4x+1) = 0 \\ \Leftrightarrow x = 0 \vee 4x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{4} \\ V = \Big\{ 0 ; \frac{-1}{4} \Big\} \\ -----------------\)
10. \(2(-6x^2+7x)=-(16x^2+10x) \\ \Leftrightarrow -12x^2+14x=-16x^2-10x \\ \Leftrightarrow -12x^2+14x+16x^2+10x= 0 \\ \Leftrightarrow 4x^2-24x=0 \\ \Leftrightarrow x(4x-24) = 0 \\ \Leftrightarrow x = 0 \vee 4x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{4} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
11. \(-7x^2-17x=0 \\ \Leftrightarrow x(-7x-17) = 0 \\ \Leftrightarrow x = 0 \vee -7x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-7} = \frac{-17}{7} \\ V = \Big\{ 0 ; \frac{-17}{7} \Big\} \\ -----------------\)
12. \(5x^2-4x=0 \\ \Leftrightarrow x(5x-4) = 0 \\ \Leftrightarrow x = 0 \vee 5x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{5} \\ V = \Big\{ \frac{4}{5}; 0 \Big\} \\ -----------------\)