Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-7x^2-24x=0\)
2. \(2(2x^2+8x)=-(-8x^2-34x)\)
3. \(2x^2-9x=0\)
4. \(-x^2+10x=4x^2+2x\)
5. \(8x^2+21x=0\)
6. \(5(-7x^2-5x)=-(34x^2+50x)\)
7. \(-x^2+19x=0\)
8. \(3(-8x^2-10x)=-(23x^2+47x)\)
9. \(-8x^2+24x=-7x^2+4x\)
10. \(-5x^2-2x=2x^2+5x\)
11. \(5(7x^2+3x)=-(-40x^2+6x)\)
12. \(15x^2-3x=7x^2-9x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-7x^2-24x=0 \\ \Leftrightarrow x(-7x-24) = 0 \\ \Leftrightarrow x = 0 \vee -7x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-7} = \frac{-24}{7} \\ V = \Big\{ 0 ; \frac{-24}{7} \Big\} \\ -----------------\)
2. \(2(2x^2+8x)=-(-8x^2-34x) \\ \Leftrightarrow 4x^2+16x=8x^2+34x \\ \Leftrightarrow 4x^2+16x-8x^2-34x= 0 \\ \Leftrightarrow -4x^2+18x=0 \\ \Leftrightarrow x(-4x+18) = 0 \\ \Leftrightarrow x = 0 \vee -4x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-4} = \frac{9}{2} \\ V = \Big\{ \frac{9}{2}; 0 \Big\} \\ -----------------\)
3. \(2x^2-9x=0 \\ \Leftrightarrow x(2x-9) = 0 \\ \Leftrightarrow x = 0 \vee 2x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{2} \\ V = \Big\{ \frac{9}{2}; 0 \Big\} \\ -----------------\)
4. \(-x^2+10x=4x^2+2x \\ \Leftrightarrow -5x^2+8x=0 \\ \Leftrightarrow x(-5x+8) = 0 \\ \Leftrightarrow x = 0 \vee -5x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-5} = \frac{8}{5} \\ V = \Big\{ \frac{8}{5}; 0 \Big\} \\ -----------------\)
5. \(8x^2+21x=0 \\ \Leftrightarrow x(8x+21) = 0 \\ \Leftrightarrow x = 0 \vee 8x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{8} \\ V = \Big\{ 0 ; \frac{-21}{8} \Big\} \\ -----------------\)
6. \(5(-7x^2-5x)=-(34x^2+50x) \\ \Leftrightarrow -35x^2-25x=-34x^2-50x \\ \Leftrightarrow -35x^2-25x+34x^2+50x= 0 \\ \Leftrightarrow -x^2-25x=0 \\ \Leftrightarrow x(-x-25) = 0 \\ \Leftrightarrow x = 0 \vee -x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-1} = -25 \\ V = \Big\{ 0 ; -25 \Big\} \\ -----------------\)
7. \(-x^2+19x=0 \\ \Leftrightarrow x(-x+19) = 0 \\ \Leftrightarrow x = 0 \vee -x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-1} = 19 \\ V = \Big\{ 19; 0 \Big\} \\ -----------------\)
8. \(3(-8x^2-10x)=-(23x^2+47x) \\ \Leftrightarrow -24x^2-30x=-23x^2-47x \\ \Leftrightarrow -24x^2-30x+23x^2+47x= 0 \\ \Leftrightarrow -x^2-17x=0 \\ \Leftrightarrow x(-x-17) = 0 \\ \Leftrightarrow x = 0 \vee -x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-1} = -17 \\ V = \Big\{ 0 ; -17 \Big\} \\ -----------------\)
9. \(-8x^2+24x=-7x^2+4x \\ \Leftrightarrow -x^2+20x=0 \\ \Leftrightarrow x(-x+20) = 0 \\ \Leftrightarrow x = 0 \vee -x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-1} = 20 \\ V = \Big\{ 20; 0 \Big\} \\ -----------------\)
10. \(-5x^2-2x=2x^2+5x \\ \Leftrightarrow -7x^2-7x=0 \\ \Leftrightarrow x(-7x-7) = 0 \\ \Leftrightarrow x = 0 \vee -7x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-7} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
11. \(5(7x^2+3x)=-(-40x^2+6x) \\ \Leftrightarrow 35x^2+15x=40x^2-6x \\ \Leftrightarrow 35x^2+15x-40x^2+6x= 0 \\ \Leftrightarrow -5x^2-21x=0 \\ \Leftrightarrow x(-5x-21) = 0 \\ \Leftrightarrow x = 0 \vee -5x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-5} = \frac{-21}{5} \\ V = \Big\{ 0 ; \frac{-21}{5} \Big\} \\ -----------------\)
12. \(15x^2-3x=7x^2-9x \\ \Leftrightarrow 8x^2+6x=0 \\ \Leftrightarrow x(8x+6) = 0 \\ \Leftrightarrow x = 0 \vee 8x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{8} = \frac{-3}{4} \\ V = \Big\{ 0 ; \frac{-3}{4} \Big\} \\ -----------------\)