Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3x^2-9x=0\)
2. \(7x^2-12x=2x^2-7x\)
3. \(12x^2+23x=7x^2+10x\)
4. \(x^2+13x=0\)
5. \(5x^2-15x=0\)
6. \(-2(-6x^2+10x)=-(-20x^2+8x)\)
7. \(-9x^2+12x=-8x^2-7x\)
8. \(-4(-10x^2-7x)=-(-39x^2-39x)\)
9. \(-7x^2+13x=-3x^2+7x\)
10. \(-3x^2-18x=-2x^2-10x\)
11. \(-3(-9x^2+9x)=-(-23x^2+2x)\)
12. \(4x^2+18x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3x^2-9x=0 \\ \Leftrightarrow x(-3x-9) = 0 \\ \Leftrightarrow x = 0 \vee -3x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-3} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
2. \(7x^2-12x=2x^2-7x \\ \Leftrightarrow 5x^2-5x=0 \\ \Leftrightarrow x(5x-5) = 0 \\ \Leftrightarrow x = 0 \vee 5x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{5} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
3. \(12x^2+23x=7x^2+10x \\ \Leftrightarrow 5x^2+13x=0 \\ \Leftrightarrow x(5x+13) = 0 \\ \Leftrightarrow x = 0 \vee 5x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{5} \\ V = \Big\{ 0 ; \frac{-13}{5} \Big\} \\ -----------------\)
4. \(x^2+13x=0 \\ \Leftrightarrow x(x+13) = 0 \\ \Leftrightarrow x = 0 \vee x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{1} = -13 \\ V = \Big\{ 0 ; -13 \Big\} \\ -----------------\)
5. \(5x^2-15x=0 \\ \Leftrightarrow x(5x-15) = 0 \\ \Leftrightarrow x = 0 \vee 5x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{5} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
6. \(-2(-6x^2+10x)=-(-20x^2+8x) \\ \Leftrightarrow 12x^2-20x=20x^2-8x \\ \Leftrightarrow 12x^2-20x-20x^2+8x= 0 \\ \Leftrightarrow -8x^2+12x=0 \\ \Leftrightarrow x(-8x+12) = 0 \\ \Leftrightarrow x = 0 \vee -8x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{-8} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
7. \(-9x^2+12x=-8x^2-7x \\ \Leftrightarrow -x^2+19x=0 \\ \Leftrightarrow x(-x+19) = 0 \\ \Leftrightarrow x = 0 \vee -x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-1} = 19 \\ V = \Big\{ 19; 0 \Big\} \\ -----------------\)
8. \(-4(-10x^2-7x)=-(-39x^2-39x) \\ \Leftrightarrow 40x^2+28x=39x^2+39x \\ \Leftrightarrow 40x^2+28x-39x^2-39x= 0 \\ \Leftrightarrow x^2+11x=0 \\ \Leftrightarrow x(x+11) = 0 \\ \Leftrightarrow x = 0 \vee x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{1} = -11 \\ V = \Big\{ 0 ; -11 \Big\} \\ -----------------\)
9. \(-7x^2+13x=-3x^2+7x \\ \Leftrightarrow -4x^2+6x=0 \\ \Leftrightarrow x(-4x+6) = 0 \\ \Leftrightarrow x = 0 \vee -4x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-4} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
10. \(-3x^2-18x=-2x^2-10x \\ \Leftrightarrow -x^2-8x=0 \\ \Leftrightarrow x(-x-8) = 0 \\ \Leftrightarrow x = 0 \vee -x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-1} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
11. \(-3(-9x^2+9x)=-(-23x^2+2x) \\ \Leftrightarrow 27x^2-27x=23x^2-2x \\ \Leftrightarrow 27x^2-27x-23x^2+2x= 0 \\ \Leftrightarrow 4x^2+25x=0 \\ \Leftrightarrow x(4x+25) = 0 \\ \Leftrightarrow x = 0 \vee 4x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{4} \\ V = \Big\{ 0 ; \frac{-25}{4} \Big\} \\ -----------------\)
12. \(4x^2+18x=0 \\ \Leftrightarrow x(4x+18) = 0 \\ \Leftrightarrow x = 0 \vee 4x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{4} = \frac{-9}{2} \\ V = \Big\{ 0 ; \frac{-9}{2} \Big\} \\ -----------------\)