Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-17x^2+17x=-10x^2+6x\)
2. \(-x^2+2x=-5x^2-2x\)
3. \(-11x^2+10x=-8x^2+4x\)
4. \(-x^2-3x=0\)
5. \(-4(-3x^2+2x)=-(-6x^2+26x)\)
6. \(-5(-9x^2+5x)=-(-52x^2+31x)\)
7. \(3(-7x^2+9x)=-(24x^2-52x)\)
8. \(4(-10x^2-8x)=-(35x^2+56x)\)
9. \(-8x^2+15x=-2x^2+7x\)
10. \(-2x^2-32x=-5x^2-8x\)
11. \(-2(-2x^2-3x)=-(2x^2+16x)\)
12. \(-4x^2+6x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-17x^2+17x=-10x^2+6x \\ \Leftrightarrow -7x^2+11x=0 \\ \Leftrightarrow x(-7x+11) = 0 \\ \Leftrightarrow x = 0 \vee -7x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-7} = \frac{11}{7} \\ V = \Big\{ \frac{11}{7}; 0 \Big\} \\ -----------------\)
2. \(-x^2+2x=-5x^2-2x \\ \Leftrightarrow 4x^2+4x=0 \\ \Leftrightarrow x(4x+4) = 0 \\ \Leftrightarrow x = 0 \vee 4x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{4} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
3. \(-11x^2+10x=-8x^2+4x \\ \Leftrightarrow -3x^2+6x=0 \\ \Leftrightarrow x(-3x+6) = 0 \\ \Leftrightarrow x = 0 \vee -3x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-3} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
4. \(-x^2-3x=0 \\ \Leftrightarrow x(-x-3) = 0 \\ \Leftrightarrow x = 0 \vee -x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-1} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
5. \(-4(-3x^2+2x)=-(-6x^2+26x) \\ \Leftrightarrow 12x^2-8x=6x^2-26x \\ \Leftrightarrow 12x^2-8x-6x^2+26x= 0 \\ \Leftrightarrow 6x^2-18x=0 \\ \Leftrightarrow x(6x-18) = 0 \\ \Leftrightarrow x = 0 \vee 6x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{6} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
6. \(-5(-9x^2+5x)=-(-52x^2+31x) \\ \Leftrightarrow 45x^2-25x=52x^2-31x \\ \Leftrightarrow 45x^2-25x-52x^2+31x= 0 \\ \Leftrightarrow -7x^2-6x=0 \\ \Leftrightarrow x(-7x-6) = 0 \\ \Leftrightarrow x = 0 \vee -7x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-7} = \frac{-6}{7} \\ V = \Big\{ 0 ; \frac{-6}{7} \Big\} \\ -----------------\)
7. \(3(-7x^2+9x)=-(24x^2-52x) \\ \Leftrightarrow -21x^2+27x=-24x^2+52x \\ \Leftrightarrow -21x^2+27x+24x^2-52x= 0 \\ \Leftrightarrow 3x^2+25x=0 \\ \Leftrightarrow x(3x+25) = 0 \\ \Leftrightarrow x = 0 \vee 3x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{3} \\ V = \Big\{ 0 ; \frac{-25}{3} \Big\} \\ -----------------\)
8. \(4(-10x^2-8x)=-(35x^2+56x) \\ \Leftrightarrow -40x^2-32x=-35x^2-56x \\ \Leftrightarrow -40x^2-32x+35x^2+56x= 0 \\ \Leftrightarrow -5x^2-24x=0 \\ \Leftrightarrow x(-5x-24) = 0 \\ \Leftrightarrow x = 0 \vee -5x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-5} = \frac{-24}{5} \\ V = \Big\{ 0 ; \frac{-24}{5} \Big\} \\ -----------------\)
9. \(-8x^2+15x=-2x^2+7x \\ \Leftrightarrow -6x^2+8x=0 \\ \Leftrightarrow x(-6x+8) = 0 \\ \Leftrightarrow x = 0 \vee -6x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-6} = \frac{4}{3} \\ V = \Big\{ \frac{4}{3}; 0 \Big\} \\ -----------------\)
10. \(-2x^2-32x=-5x^2-8x \\ \Leftrightarrow 3x^2-24x=0 \\ \Leftrightarrow x(3x-24) = 0 \\ \Leftrightarrow x = 0 \vee 3x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{3} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
11. \(-2(-2x^2-3x)=-(2x^2+16x) \\ \Leftrightarrow 4x^2+6x=-2x^2-16x \\ \Leftrightarrow 4x^2+6x+2x^2+16x= 0 \\ \Leftrightarrow 6x^2-22x=0 \\ \Leftrightarrow x(6x-22) = 0 \\ \Leftrightarrow x = 0 \vee 6x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{6} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
12. \(-4x^2+6x=0 \\ \Leftrightarrow x(-4x+6) = 0 \\ \Leftrightarrow x = 0 \vee -4x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-4} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)