Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(-8x^2+9x)=-(-38x^2+30x)\)
2. \(3(-6x^2+6x)=-(23x^2-14x)\)
3. \(-4x^2-4x=0\)
4. \(14x^2-24x=9x^2-6x\)
5. \(4(9x^2-3x)=-(-28x^2+2x)\)
6. \(-4x^2-22x=0\)
7. \(7x^2-21x=0\)
8. \(3x^2-10x=0\)
9. \(-6x^2-1x=0\)
10. \(-5(-10x^2+10x)=-(-56x^2+62x)\)
11. \(-13x^2+13x=-7x^2-5x\)
12. \(7x^2-17x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(-8x^2+9x)=-(-38x^2+30x) \\ \Leftrightarrow 40x^2-45x=38x^2-30x \\ \Leftrightarrow 40x^2-45x-38x^2+30x= 0 \\ \Leftrightarrow 2x^2+15x=0 \\ \Leftrightarrow x(2x+15) = 0 \\ \Leftrightarrow x = 0 \vee 2x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{2} \\ V = \Big\{ 0 ; \frac{-15}{2} \Big\} \\ -----------------\)
2. \(3(-6x^2+6x)=-(23x^2-14x) \\ \Leftrightarrow -18x^2+18x=-23x^2+14x \\ \Leftrightarrow -18x^2+18x+23x^2-14x= 0 \\ \Leftrightarrow 5x^2-4x=0 \\ \Leftrightarrow x(5x-4) = 0 \\ \Leftrightarrow x = 0 \vee 5x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{5} \\ V = \Big\{ \frac{4}{5}; 0 \Big\} \\ -----------------\)
3. \(-4x^2-4x=0 \\ \Leftrightarrow x(-4x-4) = 0 \\ \Leftrightarrow x = 0 \vee -4x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-4} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
4. \(14x^2-24x=9x^2-6x \\ \Leftrightarrow 5x^2-18x=0 \\ \Leftrightarrow x(5x-18) = 0 \\ \Leftrightarrow x = 0 \vee 5x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{5} \\ V = \Big\{ \frac{18}{5}; 0 \Big\} \\ -----------------\)
5. \(4(9x^2-3x)=-(-28x^2+2x) \\ \Leftrightarrow 36x^2-12x=28x^2-2x \\ \Leftrightarrow 36x^2-12x-28x^2+2x= 0 \\ \Leftrightarrow 8x^2+10x=0 \\ \Leftrightarrow x(8x+10) = 0 \\ \Leftrightarrow x = 0 \vee 8x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{8} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
6. \(-4x^2-22x=0 \\ \Leftrightarrow x(-4x-22) = 0 \\ \Leftrightarrow x = 0 \vee -4x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-4} = \frac{-11}{2} \\ V = \Big\{ 0 ; \frac{-11}{2} \Big\} \\ -----------------\)
7. \(7x^2-21x=0 \\ \Leftrightarrow x(7x-21) = 0 \\ \Leftrightarrow x = 0 \vee 7x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{7} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
8. \(3x^2-10x=0 \\ \Leftrightarrow x(3x-10) = 0 \\ \Leftrightarrow x = 0 \vee 3x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)
9. \(-6x^2-1x=0 \\ \Leftrightarrow x(-6x-1) = 0 \\ \Leftrightarrow x = 0 \vee -6x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-6} = \frac{-1}{6} \\ V = \Big\{ 0 ; \frac{-1}{6} \Big\} \\ -----------------\)
10. \(-5(-10x^2+10x)=-(-56x^2+62x) \\ \Leftrightarrow 50x^2-50x=56x^2-62x \\ \Leftrightarrow 50x^2-50x-56x^2+62x= 0 \\ \Leftrightarrow -6x^2-12x=0 \\ \Leftrightarrow x(-6x-12) = 0 \\ \Leftrightarrow x = 0 \vee -6x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-6} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
11. \(-13x^2+13x=-7x^2-5x \\ \Leftrightarrow -6x^2+18x=0 \\ \Leftrightarrow x(-6x+18) = 0 \\ \Leftrightarrow x = 0 \vee -6x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-6} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
12. \(7x^2-17x=0 \\ \Leftrightarrow x(7x-17) = 0 \\ \Leftrightarrow x = 0 \vee 7x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{7} \\ V = \Big\{ \frac{17}{7}; 0 \Big\} \\ -----------------\)