Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2-4x=2x^2+9x\)
2. \(-13x^2+3x=-8x^2-5x\)
3. \(3x^2+22x=0\)
4. \(5(-4x^2-6x)=-(22x^2+22x)\)
5. \(3x^2-16x=0\)
6. \(-4(-5x^2+8x)=-(-14x^2+31x)\)
7. \(5(8x^2+6x)=-(-45x^2-49x)\)
8. \(8x^2+17x=0\)
9. \(3(4x^2-2x)=-(-10x^2+12x)\)
10. \(-8x^2+15x=0\)
11. \(-5(-5x^2+7x)=-(-26x^2+50x)\)
12. \(7x^2-8x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2-4x=2x^2+9x \\ \Leftrightarrow x^2-13x=0 \\ \Leftrightarrow x(x-13) = 0 \\ \Leftrightarrow x = 0 \vee x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{1} = 13 \\ V = \Big\{ 13; 0 \Big\} \\ -----------------\)
2. \(-13x^2+3x=-8x^2-5x \\ \Leftrightarrow -5x^2+8x=0 \\ \Leftrightarrow x(-5x+8) = 0 \\ \Leftrightarrow x = 0 \vee -5x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-5} = \frac{8}{5} \\ V = \Big\{ \frac{8}{5}; 0 \Big\} \\ -----------------\)
3. \(3x^2+22x=0 \\ \Leftrightarrow x(3x+22) = 0 \\ \Leftrightarrow x = 0 \vee 3x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{3} \\ V = \Big\{ 0 ; \frac{-22}{3} \Big\} \\ -----------------\)
4. \(5(-4x^2-6x)=-(22x^2+22x) \\ \Leftrightarrow -20x^2-30x=-22x^2-22x \\ \Leftrightarrow -20x^2-30x+22x^2+22x= 0 \\ \Leftrightarrow 2x^2+8x=0 \\ \Leftrightarrow x(2x+8) = 0 \\ \Leftrightarrow x = 0 \vee 2x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{2} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
5. \(3x^2-16x=0 \\ \Leftrightarrow x(3x-16) = 0 \\ \Leftrightarrow x = 0 \vee 3x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{3} \\ V = \Big\{ \frac{16}{3}; 0 \Big\} \\ -----------------\)
6. \(-4(-5x^2+8x)=-(-14x^2+31x) \\ \Leftrightarrow 20x^2-32x=14x^2-31x \\ \Leftrightarrow 20x^2-32x-14x^2+31x= 0 \\ \Leftrightarrow 6x^2+1x=0 \\ \Leftrightarrow x(6x+1) = 0 \\ \Leftrightarrow x = 0 \vee 6x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{6} \\ V = \Big\{ 0 ; \frac{-1}{6} \Big\} \\ -----------------\)
7. \(5(8x^2+6x)=-(-45x^2-49x) \\ \Leftrightarrow 40x^2+30x=45x^2+49x \\ \Leftrightarrow 40x^2+30x-45x^2-49x= 0 \\ \Leftrightarrow -5x^2+19x=0 \\ \Leftrightarrow x(-5x+19) = 0 \\ \Leftrightarrow x = 0 \vee -5x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-5} = \frac{19}{5} \\ V = \Big\{ \frac{19}{5}; 0 \Big\} \\ -----------------\)
8. \(8x^2+17x=0 \\ \Leftrightarrow x(8x+17) = 0 \\ \Leftrightarrow x = 0 \vee 8x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{8} \\ V = \Big\{ 0 ; \frac{-17}{8} \Big\} \\ -----------------\)
9. \(3(4x^2-2x)=-(-10x^2+12x) \\ \Leftrightarrow 12x^2-6x=10x^2-12x \\ \Leftrightarrow 12x^2-6x-10x^2+12x= 0 \\ \Leftrightarrow 2x^2-6x=0 \\ \Leftrightarrow x(2x-6) = 0 \\ \Leftrightarrow x = 0 \vee 2x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{2} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
10. \(-8x^2+15x=0 \\ \Leftrightarrow x(-8x+15) = 0 \\ \Leftrightarrow x = 0 \vee -8x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-8} = \frac{15}{8} \\ V = \Big\{ \frac{15}{8}; 0 \Big\} \\ -----------------\)
11. \(-5(-5x^2+7x)=-(-26x^2+50x) \\ \Leftrightarrow 25x^2-35x=26x^2-50x \\ \Leftrightarrow 25x^2-35x-26x^2+50x= 0 \\ \Leftrightarrow -x^2-15x=0 \\ \Leftrightarrow x(-x-15) = 0 \\ \Leftrightarrow x = 0 \vee -x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-1} = -15 \\ V = \Big\{ 0 ; -15 \Big\} \\ -----------------\)
12. \(7x^2-8x=0 \\ \Leftrightarrow x(7x-8) = 0 \\ \Leftrightarrow x = 0 \vee 7x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{7} \\ V = \Big\{ \frac{8}{7}; 0 \Big\} \\ -----------------\)