Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(6x^2+4x)=-(-15x^2+x)\)
2. \(-2x^2+3x=0\)
3. \(-5(-3x^2+6x)=-(-8x^2+35x)\)
4. \(-5(8x^2-4x)=-(36x^2-41x)\)
5. \(-6x^2+19x=0\)
6. \(-11x^2+12x=-7x^2+2x\)
7. \(-x^2+24x=0\)
8. \(-5(-8x^2+9x)=-(-39x^2+63x)\)
9. \(-17x^2+31x=-10x^2+8x\)
10. \(-15x^2+33x=-9x^2+9x\)
11. \(3x^2-16x=-4x^2+4x\)
12. \(-6x^2+9x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(6x^2+4x)=-(-15x^2+x) \\ \Leftrightarrow 12x^2+8x=15x^2-x \\ \Leftrightarrow 12x^2+8x-15x^2+x= 0 \\ \Leftrightarrow -3x^2-9x=0 \\ \Leftrightarrow x(-3x-9) = 0 \\ \Leftrightarrow x = 0 \vee -3x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-3} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
2. \(-2x^2+3x=0 \\ \Leftrightarrow x(-2x+3) = 0 \\ \Leftrightarrow x = 0 \vee -2x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-2} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
3. \(-5(-3x^2+6x)=-(-8x^2+35x) \\ \Leftrightarrow 15x^2-30x=8x^2-35x \\ \Leftrightarrow 15x^2-30x-8x^2+35x= 0 \\ \Leftrightarrow 7x^2-5x=0 \\ \Leftrightarrow x(7x-5) = 0 \\ \Leftrightarrow x = 0 \vee 7x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{7} \\ V = \Big\{ \frac{5}{7}; 0 \Big\} \\ -----------------\)
4. \(-5(8x^2-4x)=-(36x^2-41x) \\ \Leftrightarrow -40x^2+20x=-36x^2+41x \\ \Leftrightarrow -40x^2+20x+36x^2-41x= 0 \\ \Leftrightarrow -4x^2+21x=0 \\ \Leftrightarrow x(-4x+21) = 0 \\ \Leftrightarrow x = 0 \vee -4x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-4} = \frac{21}{4} \\ V = \Big\{ \frac{21}{4}; 0 \Big\} \\ -----------------\)
5. \(-6x^2+19x=0 \\ \Leftrightarrow x(-6x+19) = 0 \\ \Leftrightarrow x = 0 \vee -6x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-6} = \frac{19}{6} \\ V = \Big\{ \frac{19}{6}; 0 \Big\} \\ -----------------\)
6. \(-11x^2+12x=-7x^2+2x \\ \Leftrightarrow -4x^2+10x=0 \\ \Leftrightarrow x(-4x+10) = 0 \\ \Leftrightarrow x = 0 \vee -4x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-4} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
7. \(-x^2+24x=0 \\ \Leftrightarrow x(-x+24) = 0 \\ \Leftrightarrow x = 0 \vee -x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-1} = 24 \\ V = \Big\{ 24; 0 \Big\} \\ -----------------\)
8. \(-5(-8x^2+9x)=-(-39x^2+63x) \\ \Leftrightarrow 40x^2-45x=39x^2-63x \\ \Leftrightarrow 40x^2-45x-39x^2+63x= 0 \\ \Leftrightarrow x^2-18x=0 \\ \Leftrightarrow x(x-18) = 0 \\ \Leftrightarrow x = 0 \vee x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{1} = 18 \\ V = \Big\{ 18; 0 \Big\} \\ -----------------\)
9. \(-17x^2+31x=-10x^2+8x \\ \Leftrightarrow -7x^2+23x=0 \\ \Leftrightarrow x(-7x+23) = 0 \\ \Leftrightarrow x = 0 \vee -7x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-7} = \frac{23}{7} \\ V = \Big\{ \frac{23}{7}; 0 \Big\} \\ -----------------\)
10. \(-15x^2+33x=-9x^2+9x \\ \Leftrightarrow -6x^2+24x=0 \\ \Leftrightarrow x(-6x+24) = 0 \\ \Leftrightarrow x = 0 \vee -6x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-6} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
11. \(3x^2-16x=-4x^2+4x \\ \Leftrightarrow 7x^2-20x=0 \\ \Leftrightarrow x(7x-20) = 0 \\ \Leftrightarrow x = 0 \vee 7x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{7} \\ V = \Big\{ \frac{20}{7}; 0 \Big\} \\ -----------------\)
12. \(-6x^2+9x=0 \\ \Leftrightarrow x(-6x+9) = 0 \\ \Leftrightarrow x = 0 \vee -6x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-6} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)