Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2-24x=0\)
2. \(-3(-4x^2+3x)=-(-13x^2+0x)\)
3. \(-2(2x^2-10x)=-(11x^2-6x)\)
4. \(-16x^2+25x=-10x^2+2x\)
5. \(7x^2+17x=0\)
6. \(6x^2+14x=0\)
7. \(4(-8x^2+9x)=-(31x^2-13x)\)
8. \(6x^2+2x=0\)
9. \(-5(2x^2+9x)=-(6x^2+46x)\)
10. \(-2(5x^2+5x)=-(6x^2+31x)\)
11. \(7x^2+21x=0\)
12. \(9x^2+17x=8x^2+8x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2-24x=0 \\ \Leftrightarrow x(-5x-24) = 0 \\ \Leftrightarrow x = 0 \vee -5x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-5} = \frac{-24}{5} \\ V = \Big\{ 0 ; \frac{-24}{5} \Big\} \\ -----------------\)
2. \(-3(-4x^2+3x)=-(-13x^2+0x) \\ \Leftrightarrow 12x^2-9x=13x^2+0x \\ \Leftrightarrow 12x^2-9x-13x^2+0x= 0 \\ \Leftrightarrow -x^2+9x=0 \\ \Leftrightarrow x(-x+9) = 0 \\ \Leftrightarrow x = 0 \vee -x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-1} = 9 \\ V = \Big\{ 9; 0 \Big\} \\ -----------------\)
3. \(-2(2x^2-10x)=-(11x^2-6x) \\ \Leftrightarrow -4x^2+20x=-11x^2+6x \\ \Leftrightarrow -4x^2+20x+11x^2-6x= 0 \\ \Leftrightarrow 7x^2-14x=0 \\ \Leftrightarrow x(7x-14) = 0 \\ \Leftrightarrow x = 0 \vee 7x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{7} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
4. \(-16x^2+25x=-10x^2+2x \\ \Leftrightarrow -6x^2+23x=0 \\ \Leftrightarrow x(-6x+23) = 0 \\ \Leftrightarrow x = 0 \vee -6x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-6} = \frac{23}{6} \\ V = \Big\{ \frac{23}{6}; 0 \Big\} \\ -----------------\)
5. \(7x^2+17x=0 \\ \Leftrightarrow x(7x+17) = 0 \\ \Leftrightarrow x = 0 \vee 7x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{7} \\ V = \Big\{ 0 ; \frac{-17}{7} \Big\} \\ -----------------\)
6. \(6x^2+14x=0 \\ \Leftrightarrow x(6x+14) = 0 \\ \Leftrightarrow x = 0 \vee 6x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{6} = \frac{-7}{3} \\ V = \Big\{ 0 ; \frac{-7}{3} \Big\} \\ -----------------\)
7. \(4(-8x^2+9x)=-(31x^2-13x) \\ \Leftrightarrow -32x^2+36x=-31x^2+13x \\ \Leftrightarrow -32x^2+36x+31x^2-13x= 0 \\ \Leftrightarrow -x^2-23x=0 \\ \Leftrightarrow x(-x-23) = 0 \\ \Leftrightarrow x = 0 \vee -x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-1} = -23 \\ V = \Big\{ 0 ; -23 \Big\} \\ -----------------\)
8. \(6x^2+2x=0 \\ \Leftrightarrow x(6x+2) = 0 \\ \Leftrightarrow x = 0 \vee 6x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{6} = \frac{-1}{3} \\ V = \Big\{ 0 ; \frac{-1}{3} \Big\} \\ -----------------\)
9. \(-5(2x^2+9x)=-(6x^2+46x) \\ \Leftrightarrow -10x^2-45x=-6x^2-46x \\ \Leftrightarrow -10x^2-45x+6x^2+46x= 0 \\ \Leftrightarrow -4x^2-1x=0 \\ \Leftrightarrow x(-4x-1) = 0 \\ \Leftrightarrow x = 0 \vee -4x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-4} = \frac{-1}{4} \\ V = \Big\{ 0 ; \frac{-1}{4} \Big\} \\ -----------------\)
10. \(-2(5x^2+5x)=-(6x^2+31x) \\ \Leftrightarrow -10x^2-10x=-6x^2-31x \\ \Leftrightarrow -10x^2-10x+6x^2+31x= 0 \\ \Leftrightarrow -4x^2-21x=0 \\ \Leftrightarrow x(-4x-21) = 0 \\ \Leftrightarrow x = 0 \vee -4x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-4} = \frac{-21}{4} \\ V = \Big\{ 0 ; \frac{-21}{4} \Big\} \\ -----------------\)
11. \(7x^2+21x=0 \\ \Leftrightarrow x(7x+21) = 0 \\ \Leftrightarrow x = 0 \vee 7x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{7} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
12. \(9x^2+17x=8x^2+8x \\ \Leftrightarrow x^2+9x=0 \\ \Leftrightarrow x(x+9) = 0 \\ \Leftrightarrow x = 0 \vee x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{1} = -9 \\ V = \Big\{ 0 ; -9 \Big\} \\ -----------------\)