Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(6x^2+1x=0\)
2. \(4(-2x^2-10x)=-(0x^2+42x)\)
3. \(-4x^2+x=-9x^2+3x\)
4. \(3(-8x^2+6x)=-(29x^2-17x)\)
5. \(-3(9x^2+2x)=-(22x^2+19x)\)
6. \(2(-3x^2+4x)=-(-x^2-29x)\)
7. \(-x^2+21x=-6x^2+4x\)
8. \(5(6x^2-10x)=-(-32x^2+26x)\)
9. \(-3(3x^2+8x)=-(17x^2+23x)\)
10. \(4x^2-2x=0\)
11. \(-x^2-13x=0\)
12. \(-9x^2-27x=-10x^2-2x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(6x^2+1x=0 \\ \Leftrightarrow x(6x+1) = 0 \\ \Leftrightarrow x = 0 \vee 6x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{6} \\ V = \Big\{ 0 ; \frac{-1}{6} \Big\} \\ -----------------\)
2. \(4(-2x^2-10x)=-(0x^2+42x) \\ \Leftrightarrow -8x^2-40x=0x^2-42x \\ \Leftrightarrow -8x^2-40x+0x^2+42x= 0 \\ \Leftrightarrow -8x^2-2x=0 \\ \Leftrightarrow x(-8x-2) = 0 \\ \Leftrightarrow x = 0 \vee -8x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-8} = \frac{-1}{4} \\ V = \Big\{ 0 ; \frac{-1}{4} \Big\} \\ -----------------\)
3. \(-4x^2+x=-9x^2+3x \\ \Leftrightarrow 5x^2-2x=0 \\ \Leftrightarrow x(5x-2) = 0 \\ \Leftrightarrow x = 0 \vee 5x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{5} \\ V = \Big\{ \frac{2}{5}; 0 \Big\} \\ -----------------\)
4. \(3(-8x^2+6x)=-(29x^2-17x) \\ \Leftrightarrow -24x^2+18x=-29x^2+17x \\ \Leftrightarrow -24x^2+18x+29x^2-17x= 0 \\ \Leftrightarrow 5x^2-1x=0 \\ \Leftrightarrow x(5x-1) = 0 \\ \Leftrightarrow x = 0 \vee 5x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{5} \\ V = \Big\{ \frac{1}{5}; 0 \Big\} \\ -----------------\)
5. \(-3(9x^2+2x)=-(22x^2+19x) \\ \Leftrightarrow -27x^2-6x=-22x^2-19x \\ \Leftrightarrow -27x^2-6x+22x^2+19x= 0 \\ \Leftrightarrow -5x^2-13x=0 \\ \Leftrightarrow x(-5x-13) = 0 \\ \Leftrightarrow x = 0 \vee -5x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-5} = \frac{-13}{5} \\ V = \Big\{ 0 ; \frac{-13}{5} \Big\} \\ -----------------\)
6. \(2(-3x^2+4x)=-(-x^2-29x) \\ \Leftrightarrow -6x^2+8x=x^2+29x \\ \Leftrightarrow -6x^2+8x-x^2-29x= 0 \\ \Leftrightarrow -7x^2+21x=0 \\ \Leftrightarrow x(-7x+21) = 0 \\ \Leftrightarrow x = 0 \vee -7x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-7} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
7. \(-x^2+21x=-6x^2+4x \\ \Leftrightarrow 5x^2+17x=0 \\ \Leftrightarrow x(5x+17) = 0 \\ \Leftrightarrow x = 0 \vee 5x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{5} \\ V = \Big\{ 0 ; \frac{-17}{5} \Big\} \\ -----------------\)
8. \(5(6x^2-10x)=-(-32x^2+26x) \\ \Leftrightarrow 30x^2-50x=32x^2-26x \\ \Leftrightarrow 30x^2-50x-32x^2+26x= 0 \\ \Leftrightarrow -2x^2+24x=0 \\ \Leftrightarrow x(-2x+24) = 0 \\ \Leftrightarrow x = 0 \vee -2x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-2} = 12 \\ V = \Big\{ 12; 0 \Big\} \\ -----------------\)
9. \(-3(3x^2+8x)=-(17x^2+23x) \\ \Leftrightarrow -9x^2-24x=-17x^2-23x \\ \Leftrightarrow -9x^2-24x+17x^2+23x= 0 \\ \Leftrightarrow 8x^2+1x=0 \\ \Leftrightarrow x(8x+1) = 0 \\ \Leftrightarrow x = 0 \vee 8x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{8} \\ V = \Big\{ 0 ; \frac{-1}{8} \Big\} \\ -----------------\)
10. \(4x^2-2x=0 \\ \Leftrightarrow x(4x-2) = 0 \\ \Leftrightarrow x = 0 \vee 4x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{4} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
11. \(-x^2-13x=0 \\ \Leftrightarrow x(-x-13) = 0 \\ \Leftrightarrow x = 0 \vee -x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-1} = -13 \\ V = \Big\{ 0 ; -13 \Big\} \\ -----------------\)
12. \(-9x^2-27x=-10x^2-2x \\ \Leftrightarrow x^2-25x=0 \\ \Leftrightarrow x(x-25) = 0 \\ \Leftrightarrow x = 0 \vee x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{1} = 25 \\ V = \Big\{ 25; 0 \Big\} \\ -----------------\)