Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2+21x=0\)
2. \(13x^2+8x=10x^2-9x\)
3. \(4x^2-15x=0\)
4. \(6x^2+9x=0\)
5. \(3(-3x^2+7x)=-(5x^2-23x)\)
6. \(5(-10x^2-5x)=-(45x^2+47x)\)
7. \(5x^2+3x=0\)
8. \(-2x^2-16x=-8x^2-10x\)
9. \(-6x^2+15x=0\)
10. \(-4(3x^2+9x)=-(6x^2+61x)\)
11. \(-2x^2-24x=0\)
12. \(8x^2-9x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2+21x=0 \\ \Leftrightarrow x(x+21) = 0 \\ \Leftrightarrow x = 0 \vee x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{1} = -21 \\ V = \Big\{ 0 ; -21 \Big\} \\ -----------------\)
2. \(13x^2+8x=10x^2-9x \\ \Leftrightarrow 3x^2+17x=0 \\ \Leftrightarrow x(3x+17) = 0 \\ \Leftrightarrow x = 0 \vee 3x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{3} \\ V = \Big\{ 0 ; \frac{-17}{3} \Big\} \\ -----------------\)
3. \(4x^2-15x=0 \\ \Leftrightarrow x(4x-15) = 0 \\ \Leftrightarrow x = 0 \vee 4x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{4} \\ V = \Big\{ \frac{15}{4}; 0 \Big\} \\ -----------------\)
4. \(6x^2+9x=0 \\ \Leftrightarrow x(6x+9) = 0 \\ \Leftrightarrow x = 0 \vee 6x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{6} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
5. \(3(-3x^2+7x)=-(5x^2-23x) \\ \Leftrightarrow -9x^2+21x=-5x^2+23x \\ \Leftrightarrow -9x^2+21x+5x^2-23x= 0 \\ \Leftrightarrow -4x^2+2x=0 \\ \Leftrightarrow x(-4x+2) = 0 \\ \Leftrightarrow x = 0 \vee -4x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-4} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
6. \(5(-10x^2-5x)=-(45x^2+47x) \\ \Leftrightarrow -50x^2-25x=-45x^2-47x \\ \Leftrightarrow -50x^2-25x+45x^2+47x= 0 \\ \Leftrightarrow -5x^2-22x=0 \\ \Leftrightarrow x(-5x-22) = 0 \\ \Leftrightarrow x = 0 \vee -5x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-5} = \frac{-22}{5} \\ V = \Big\{ 0 ; \frac{-22}{5} \Big\} \\ -----------------\)
7. \(5x^2+3x=0 \\ \Leftrightarrow x(5x+3) = 0 \\ \Leftrightarrow x = 0 \vee 5x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{5} \\ V = \Big\{ 0 ; \frac{-3}{5} \Big\} \\ -----------------\)
8. \(-2x^2-16x=-8x^2-10x \\ \Leftrightarrow 6x^2-6x=0 \\ \Leftrightarrow x(6x-6) = 0 \\ \Leftrightarrow x = 0 \vee 6x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{6} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
9. \(-6x^2+15x=0 \\ \Leftrightarrow x(-6x+15) = 0 \\ \Leftrightarrow x = 0 \vee -6x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-6} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
10. \(-4(3x^2+9x)=-(6x^2+61x) \\ \Leftrightarrow -12x^2-36x=-6x^2-61x \\ \Leftrightarrow -12x^2-36x+6x^2+61x= 0 \\ \Leftrightarrow -6x^2-25x=0 \\ \Leftrightarrow x(-6x-25) = 0 \\ \Leftrightarrow x = 0 \vee -6x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-6} = \frac{-25}{6} \\ V = \Big\{ 0 ; \frac{-25}{6} \Big\} \\ -----------------\)
11. \(-2x^2-24x=0 \\ \Leftrightarrow x(-2x-24) = 0 \\ \Leftrightarrow x = 0 \vee -2x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-2} = -12 \\ V = \Big\{ 0 ; -12 \Big\} \\ -----------------\)
12. \(8x^2-9x=0 \\ \Leftrightarrow x(8x-9) = 0 \\ \Leftrightarrow x = 0 \vee 8x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{8} \\ V = \Big\{ \frac{9}{8}; 0 \Big\} \\ -----------------\)