Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(-5x^2+7x)=-(32x^2-41x)\)
2. \(3x^2+16x=0\)
3. \(2x^2+25x=0\)
4. \(-15x^2-21x=-10x^2-5x\)
5. \(5(8x^2-6x)=-(-46x^2+14x)\)
6. \(4(5x^2-10x)=-(-22x^2+44x)\)
7. \(-3(-5x^2+8x)=-(-13x^2+6x)\)
8. \(4(-2x^2-9x)=-(14x^2+39x)\)
9. \(-5x^2+11x=0\)
10. \(-6x^2-23x=0\)
11. \(x^2-23x=0\)
12. \(4(3x^2+7x)=-(-6x^2-37x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(-5x^2+7x)=-(32x^2-41x) \\ \Leftrightarrow -25x^2+35x=-32x^2+41x \\ \Leftrightarrow -25x^2+35x+32x^2-41x= 0 \\ \Leftrightarrow 7x^2+6x=0 \\ \Leftrightarrow x(7x+6) = 0 \\ \Leftrightarrow x = 0 \vee 7x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{7} \\ V = \Big\{ 0 ; \frac{-6}{7} \Big\} \\ -----------------\)
2. \(3x^2+16x=0 \\ \Leftrightarrow x(3x+16) = 0 \\ \Leftrightarrow x = 0 \vee 3x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{3} \\ V = \Big\{ 0 ; \frac{-16}{3} \Big\} \\ -----------------\)
3. \(2x^2+25x=0 \\ \Leftrightarrow x(2x+25) = 0 \\ \Leftrightarrow x = 0 \vee 2x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{2} \\ V = \Big\{ 0 ; \frac{-25}{2} \Big\} \\ -----------------\)
4. \(-15x^2-21x=-10x^2-5x \\ \Leftrightarrow -5x^2-16x=0 \\ \Leftrightarrow x(-5x-16) = 0 \\ \Leftrightarrow x = 0 \vee -5x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-5} = \frac{-16}{5} \\ V = \Big\{ 0 ; \frac{-16}{5} \Big\} \\ -----------------\)
5. \(5(8x^2-6x)=-(-46x^2+14x) \\ \Leftrightarrow 40x^2-30x=46x^2-14x \\ \Leftrightarrow 40x^2-30x-46x^2+14x= 0 \\ \Leftrightarrow -6x^2+16x=0 \\ \Leftrightarrow x(-6x+16) = 0 \\ \Leftrightarrow x = 0 \vee -6x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-6} = \frac{8}{3} \\ V = \Big\{ \frac{8}{3}; 0 \Big\} \\ -----------------\)
6. \(4(5x^2-10x)=-(-22x^2+44x) \\ \Leftrightarrow 20x^2-40x=22x^2-44x \\ \Leftrightarrow 20x^2-40x-22x^2+44x= 0 \\ \Leftrightarrow -2x^2-4x=0 \\ \Leftrightarrow x(-2x-4) = 0 \\ \Leftrightarrow x = 0 \vee -2x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-2} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
7. \(-3(-5x^2+8x)=-(-13x^2+6x) \\ \Leftrightarrow 15x^2-24x=13x^2-6x \\ \Leftrightarrow 15x^2-24x-13x^2+6x= 0 \\ \Leftrightarrow 2x^2+18x=0 \\ \Leftrightarrow x(2x+18) = 0 \\ \Leftrightarrow x = 0 \vee 2x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{2} = -9 \\ V = \Big\{ 0 ; -9 \Big\} \\ -----------------\)
8. \(4(-2x^2-9x)=-(14x^2+39x) \\ \Leftrightarrow -8x^2-36x=-14x^2-39x \\ \Leftrightarrow -8x^2-36x+14x^2+39x= 0 \\ \Leftrightarrow 6x^2-3x=0 \\ \Leftrightarrow x(6x-3) = 0 \\ \Leftrightarrow x = 0 \vee 6x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{6} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
9. \(-5x^2+11x=0 \\ \Leftrightarrow x(-5x+11) = 0 \\ \Leftrightarrow x = 0 \vee -5x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-5} = \frac{11}{5} \\ V = \Big\{ \frac{11}{5}; 0 \Big\} \\ -----------------\)
10. \(-6x^2-23x=0 \\ \Leftrightarrow x(-6x-23) = 0 \\ \Leftrightarrow x = 0 \vee -6x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-6} = \frac{-23}{6} \\ V = \Big\{ 0 ; \frac{-23}{6} \Big\} \\ -----------------\)
11. \(x^2-23x=0 \\ \Leftrightarrow x(x-23) = 0 \\ \Leftrightarrow x = 0 \vee x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{1} = 23 \\ V = \Big\{ 23; 0 \Big\} \\ -----------------\)
12. \(4(3x^2+7x)=-(-6x^2-37x) \\ \Leftrightarrow 12x^2+28x=6x^2+37x \\ \Leftrightarrow 12x^2+28x-6x^2-37x= 0 \\ \Leftrightarrow 6x^2+9x=0 \\ \Leftrightarrow x(6x+9) = 0 \\ \Leftrightarrow x = 0 \vee 6x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{6} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)