Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2+0x=0\)
2. \(-6x^2+8x=0\)
3. \(-3(6x^2-7x)=-(26x^2-26x)\)
4. \(7x^2+13x=0\)
5. \(-5x^2-27x=-10x^2-6x\)
6. \(-3x^2+13x=0\)
7. \(5(-7x^2+5x)=-(36x^2+0x)\)
8. \(4(6x^2+5x)=-(-17x^2-26x)\)
9. \(-13x^2-27x=-8x^2-8x\)
10. \(-5(3x^2+5x)=-(21x^2+28x)\)
11. \(3x^2+4x=0\)
12. \(3(3x^2+4x)=-(-16x^2-14x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2+0x=0 \\ \Leftrightarrow 5x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{5} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-6x^2+8x=0 \\ \Leftrightarrow x(-6x+8) = 0 \\ \Leftrightarrow x = 0 \vee -6x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-6} = \frac{4}{3} \\ V = \Big\{ \frac{4}{3}; 0 \Big\} \\ -----------------\)
3. \(-3(6x^2-7x)=-(26x^2-26x) \\ \Leftrightarrow -18x^2+21x=-26x^2+26x \\ \Leftrightarrow -18x^2+21x+26x^2-26x= 0 \\ \Leftrightarrow 8x^2+5x=0 \\ \Leftrightarrow x(8x+5) = 0 \\ \Leftrightarrow x = 0 \vee 8x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{8} \\ V = \Big\{ 0 ; \frac{-5}{8} \Big\} \\ -----------------\)
4. \(7x^2+13x=0 \\ \Leftrightarrow x(7x+13) = 0 \\ \Leftrightarrow x = 0 \vee 7x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{7} \\ V = \Big\{ 0 ; \frac{-13}{7} \Big\} \\ -----------------\)
5. \(-5x^2-27x=-10x^2-6x \\ \Leftrightarrow 5x^2-21x=0 \\ \Leftrightarrow x(5x-21) = 0 \\ \Leftrightarrow x = 0 \vee 5x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{5} \\ V = \Big\{ \frac{21}{5}; 0 \Big\} \\ -----------------\)
6. \(-3x^2+13x=0 \\ \Leftrightarrow x(-3x+13) = 0 \\ \Leftrightarrow x = 0 \vee -3x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-3} = \frac{13}{3} \\ V = \Big\{ \frac{13}{3}; 0 \Big\} \\ -----------------\)
7. \(5(-7x^2+5x)=-(36x^2+0x) \\ \Leftrightarrow -35x^2+25x=-36x^2+0x \\ \Leftrightarrow -35x^2+25x+36x^2+0x= 0 \\ \Leftrightarrow x^2-25x=0 \\ \Leftrightarrow x(x-25) = 0 \\ \Leftrightarrow x = 0 \vee x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{1} = 25 \\ V = \Big\{ 25; 0 \Big\} \\ -----------------\)
8. \(4(6x^2+5x)=-(-17x^2-26x) \\ \Leftrightarrow 24x^2+20x=17x^2+26x \\ \Leftrightarrow 24x^2+20x-17x^2-26x= 0 \\ \Leftrightarrow 7x^2+6x=0 \\ \Leftrightarrow x(7x+6) = 0 \\ \Leftrightarrow x = 0 \vee 7x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{7} \\ V = \Big\{ 0 ; \frac{-6}{7} \Big\} \\ -----------------\)
9. \(-13x^2-27x=-8x^2-8x \\ \Leftrightarrow -5x^2-19x=0 \\ \Leftrightarrow x(-5x-19) = 0 \\ \Leftrightarrow x = 0 \vee -5x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-5} = \frac{-19}{5} \\ V = \Big\{ 0 ; \frac{-19}{5} \Big\} \\ -----------------\)
10. \(-5(3x^2+5x)=-(21x^2+28x) \\ \Leftrightarrow -15x^2-25x=-21x^2-28x \\ \Leftrightarrow -15x^2-25x+21x^2+28x= 0 \\ \Leftrightarrow 6x^2-3x=0 \\ \Leftrightarrow x(6x-3) = 0 \\ \Leftrightarrow x = 0 \vee 6x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{6} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
11. \(3x^2+4x=0 \\ \Leftrightarrow x(3x+4) = 0 \\ \Leftrightarrow x = 0 \vee 3x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{3} \\ V = \Big\{ 0 ; \frac{-4}{3} \Big\} \\ -----------------\)
12. \(3(3x^2+4x)=-(-16x^2-14x) \\ \Leftrightarrow 9x^2+12x=16x^2+14x \\ \Leftrightarrow 9x^2+12x-16x^2-14x= 0 \\ \Leftrightarrow -7x^2+2x=0 \\ \Leftrightarrow x(-7x+2) = 0 \\ \Leftrightarrow x = 0 \vee -7x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-7} = \frac{2}{7} \\ V = \Big\{ \frac{2}{7}; 0 \Big\} \\ -----------------\)