Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(-2x^2-7x)=-(-12x^2-x)\)
2. \(-2x^2+19x=0\)
3. \(-5x^2-4x=0\)
4. \(6x^2-7x=0\)
5. \(-4x^2-15x=0\)
6. \(8x^2-6x=0\)
7. \(-2x^2+7x=-6x^2+5x\)
8. \(-5(8x^2-4x)=-(42x^2-26x)\)
9. \(3(-9x^2-3x)=-(21x^2-16x)\)
10. \(-x^2+16x=0\)
11. \(-8x^2-1x=0\)
12. \(-4x^2+3x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(-2x^2-7x)=-(-12x^2-x) \\ \Leftrightarrow 4x^2+14x=12x^2+x \\ \Leftrightarrow 4x^2+14x-12x^2-x= 0 \\ \Leftrightarrow -8x^2-13x=0 \\ \Leftrightarrow x(-8x-13) = 0 \\ \Leftrightarrow x = 0 \vee -8x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-8} = \frac{-13}{8} \\ V = \Big\{ 0 ; \frac{-13}{8} \Big\} \\ -----------------\)
2. \(-2x^2+19x=0 \\ \Leftrightarrow x(-2x+19) = 0 \\ \Leftrightarrow x = 0 \vee -2x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-2} = \frac{19}{2} \\ V = \Big\{ \frac{19}{2}; 0 \Big\} \\ -----------------\)
3. \(-5x^2-4x=0 \\ \Leftrightarrow x(-5x-4) = 0 \\ \Leftrightarrow x = 0 \vee -5x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-5} = \frac{-4}{5} \\ V = \Big\{ 0 ; \frac{-4}{5} \Big\} \\ -----------------\)
4. \(6x^2-7x=0 \\ \Leftrightarrow x(6x-7) = 0 \\ \Leftrightarrow x = 0 \vee 6x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{6} \\ V = \Big\{ \frac{7}{6}; 0 \Big\} \\ -----------------\)
5. \(-4x^2-15x=0 \\ \Leftrightarrow x(-4x-15) = 0 \\ \Leftrightarrow x = 0 \vee -4x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-4} = \frac{-15}{4} \\ V = \Big\{ 0 ; \frac{-15}{4} \Big\} \\ -----------------\)
6. \(8x^2-6x=0 \\ \Leftrightarrow x(8x-6) = 0 \\ \Leftrightarrow x = 0 \vee 8x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{8} = \frac{3}{4} \\ V = \Big\{ \frac{3}{4}; 0 \Big\} \\ -----------------\)
7. \(-2x^2+7x=-6x^2+5x \\ \Leftrightarrow 4x^2+2x=0 \\ \Leftrightarrow x(4x+2) = 0 \\ \Leftrightarrow x = 0 \vee 4x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{4} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
8. \(-5(8x^2-4x)=-(42x^2-26x) \\ \Leftrightarrow -40x^2+20x=-42x^2+26x \\ \Leftrightarrow -40x^2+20x+42x^2-26x= 0 \\ \Leftrightarrow 2x^2+6x=0 \\ \Leftrightarrow x(2x+6) = 0 \\ \Leftrightarrow x = 0 \vee 2x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{2} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
9. \(3(-9x^2-3x)=-(21x^2-16x) \\ \Leftrightarrow -27x^2-9x=-21x^2+16x \\ \Leftrightarrow -27x^2-9x+21x^2-16x= 0 \\ \Leftrightarrow -6x^2+25x=0 \\ \Leftrightarrow x(-6x+25) = 0 \\ \Leftrightarrow x = 0 \vee -6x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-6} = \frac{25}{6} \\ V = \Big\{ \frac{25}{6}; 0 \Big\} \\ -----------------\)
10. \(-x^2+16x=0 \\ \Leftrightarrow x(-x+16) = 0 \\ \Leftrightarrow x = 0 \vee -x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-1} = 16 \\ V = \Big\{ 16; 0 \Big\} \\ -----------------\)
11. \(-8x^2-1x=0 \\ \Leftrightarrow x(-8x-1) = 0 \\ \Leftrightarrow x = 0 \vee -8x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-8} = \frac{-1}{8} \\ V = \Big\{ 0 ; \frac{-1}{8} \Big\} \\ -----------------\)
12. \(-4x^2+3x=0 \\ \Leftrightarrow x(-4x+3) = 0 \\ \Leftrightarrow x = 0 \vee -4x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-4} = \frac{3}{4} \\ V = \Big\{ \frac{3}{4}; 0 \Big\} \\ -----------------\)