Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(3x^2-5x)=-(7x^2-23x)\)
2. \(-5x^2-5x=0\)
3. \(-3(-7x^2+9x)=-(-23x^2+15x)\)
4. \(-2(9x^2+6x)=-(12x^2+16x)\)
5. \(4x^2-8x=0\)
6. \(-5x^2+14x=-7x^2+4x\)
7. \(-5x^2+13x=0\)
8. \(5x^2-21x=4x^2-3x\)
9. \(7x^2-4x=0\)
10. \(-3x^2+22x=0\)
11. \(12x^2-9x=5x^2-2x\)
12. \(-2x^2-12x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(3x^2-5x)=-(7x^2-23x) \\ \Leftrightarrow -6x^2+10x=-7x^2+23x \\ \Leftrightarrow -6x^2+10x+7x^2-23x= 0 \\ \Leftrightarrow x^2+13x=0 \\ \Leftrightarrow x(x+13) = 0 \\ \Leftrightarrow x = 0 \vee x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{1} = -13 \\ V = \Big\{ 0 ; -13 \Big\} \\ -----------------\)
2. \(-5x^2-5x=0 \\ \Leftrightarrow x(-5x-5) = 0 \\ \Leftrightarrow x = 0 \vee -5x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-5} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
3. \(-3(-7x^2+9x)=-(-23x^2+15x) \\ \Leftrightarrow 21x^2-27x=23x^2-15x \\ \Leftrightarrow 21x^2-27x-23x^2+15x= 0 \\ \Leftrightarrow -2x^2+12x=0 \\ \Leftrightarrow x(-2x+12) = 0 \\ \Leftrightarrow x = 0 \vee -2x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{-2} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
4. \(-2(9x^2+6x)=-(12x^2+16x) \\ \Leftrightarrow -18x^2-12x=-12x^2-16x \\ \Leftrightarrow -18x^2-12x+12x^2+16x= 0 \\ \Leftrightarrow -6x^2-4x=0 \\ \Leftrightarrow x(-6x-4) = 0 \\ \Leftrightarrow x = 0 \vee -6x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-6} = \frac{-2}{3} \\ V = \Big\{ 0 ; \frac{-2}{3} \Big\} \\ -----------------\)
5. \(4x^2-8x=0 \\ \Leftrightarrow x(4x-8) = 0 \\ \Leftrightarrow x = 0 \vee 4x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{4} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
6. \(-5x^2+14x=-7x^2+4x \\ \Leftrightarrow 2x^2+10x=0 \\ \Leftrightarrow x(2x+10) = 0 \\ \Leftrightarrow x = 0 \vee 2x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{2} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
7. \(-5x^2+13x=0 \\ \Leftrightarrow x(-5x+13) = 0 \\ \Leftrightarrow x = 0 \vee -5x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-5} = \frac{13}{5} \\ V = \Big\{ \frac{13}{5}; 0 \Big\} \\ -----------------\)
8. \(5x^2-21x=4x^2-3x \\ \Leftrightarrow x^2-18x=0 \\ \Leftrightarrow x(x-18) = 0 \\ \Leftrightarrow x = 0 \vee x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{1} = 18 \\ V = \Big\{ 18; 0 \Big\} \\ -----------------\)
9. \(7x^2-4x=0 \\ \Leftrightarrow x(7x-4) = 0 \\ \Leftrightarrow x = 0 \vee 7x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{7} \\ V = \Big\{ \frac{4}{7}; 0 \Big\} \\ -----------------\)
10. \(-3x^2+22x=0 \\ \Leftrightarrow x(-3x+22) = 0 \\ \Leftrightarrow x = 0 \vee -3x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-3} = \frac{22}{3} \\ V = \Big\{ \frac{22}{3}; 0 \Big\} \\ -----------------\)
11. \(12x^2-9x=5x^2-2x \\ \Leftrightarrow 7x^2-7x=0 \\ \Leftrightarrow x(7x-7) = 0 \\ \Leftrightarrow x = 0 \vee 7x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{7} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
12. \(-2x^2-12x=0 \\ \Leftrightarrow x(-2x-12) = 0 \\ \Leftrightarrow x = 0 \vee -2x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-2} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)