Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(8x^2+17x=0\)
2. \(-7x^2-10x=0\)
3. \(7x^2-10x=0\)
4. \(5(-4x^2-10x)=-(13x^2+44x)\)
5. \(-5x^2-22x=-9x^2-6x\)
6. \(-4(9x^2+4x)=-(37x^2-8x)\)
7. \(-2x^2+4x=0\)
8. \(5(7x^2+3x)=-(-39x^2-28x)\)
9. \(-4(-2x^2+10x)=-(-2x^2+16x)\)
10. \(4(-9x^2-6x)=-(34x^2+44x)\)
11. \(-15x^2-9x=-9x^2-2x\)
12. \(-2(5x^2+3x)=-(18x^2+31x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(8x^2+17x=0 \\ \Leftrightarrow x(8x+17) = 0 \\ \Leftrightarrow x = 0 \vee 8x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{8} \\ V = \Big\{ 0 ; \frac{-17}{8} \Big\} \\ -----------------\)
2. \(-7x^2-10x=0 \\ \Leftrightarrow x(-7x-10) = 0 \\ \Leftrightarrow x = 0 \vee -7x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-7} = \frac{-10}{7} \\ V = \Big\{ 0 ; \frac{-10}{7} \Big\} \\ -----------------\)
3. \(7x^2-10x=0 \\ \Leftrightarrow x(7x-10) = 0 \\ \Leftrightarrow x = 0 \vee 7x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{7} \\ V = \Big\{ \frac{10}{7}; 0 \Big\} \\ -----------------\)
4. \(5(-4x^2-10x)=-(13x^2+44x) \\ \Leftrightarrow -20x^2-50x=-13x^2-44x \\ \Leftrightarrow -20x^2-50x+13x^2+44x= 0 \\ \Leftrightarrow -7x^2+6x=0 \\ \Leftrightarrow x(-7x+6) = 0 \\ \Leftrightarrow x = 0 \vee -7x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-7} = \frac{6}{7} \\ V = \Big\{ \frac{6}{7}; 0 \Big\} \\ -----------------\)
5. \(-5x^2-22x=-9x^2-6x \\ \Leftrightarrow 4x^2-16x=0 \\ \Leftrightarrow x(4x-16) = 0 \\ \Leftrightarrow x = 0 \vee 4x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{4} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
6. \(-4(9x^2+4x)=-(37x^2-8x) \\ \Leftrightarrow -36x^2-16x=-37x^2+8x \\ \Leftrightarrow -36x^2-16x+37x^2-8x= 0 \\ \Leftrightarrow x^2+24x=0 \\ \Leftrightarrow x(x+24) = 0 \\ \Leftrightarrow x = 0 \vee x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{1} = -24 \\ V = \Big\{ 0 ; -24 \Big\} \\ -----------------\)
7. \(-2x^2+4x=0 \\ \Leftrightarrow x(-2x+4) = 0 \\ \Leftrightarrow x = 0 \vee -2x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-2} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
8. \(5(7x^2+3x)=-(-39x^2-28x) \\ \Leftrightarrow 35x^2+15x=39x^2+28x \\ \Leftrightarrow 35x^2+15x-39x^2-28x= 0 \\ \Leftrightarrow -4x^2+13x=0 \\ \Leftrightarrow x(-4x+13) = 0 \\ \Leftrightarrow x = 0 \vee -4x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-4} = \frac{13}{4} \\ V = \Big\{ \frac{13}{4}; 0 \Big\} \\ -----------------\)
9. \(-4(-2x^2+10x)=-(-2x^2+16x) \\ \Leftrightarrow 8x^2-40x=2x^2-16x \\ \Leftrightarrow 8x^2-40x-2x^2+16x= 0 \\ \Leftrightarrow 6x^2+24x=0 \\ \Leftrightarrow x(6x+24) = 0 \\ \Leftrightarrow x = 0 \vee 6x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{6} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
10. \(4(-9x^2-6x)=-(34x^2+44x) \\ \Leftrightarrow -36x^2-24x=-34x^2-44x \\ \Leftrightarrow -36x^2-24x+34x^2+44x= 0 \\ \Leftrightarrow -2x^2-20x=0 \\ \Leftrightarrow x(-2x-20) = 0 \\ \Leftrightarrow x = 0 \vee -2x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-2} = -10 \\ V = \Big\{ 0 ; -10 \Big\} \\ -----------------\)
11. \(-15x^2-9x=-9x^2-2x \\ \Leftrightarrow -6x^2-7x=0 \\ \Leftrightarrow x(-6x-7) = 0 \\ \Leftrightarrow x = 0 \vee -6x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-6} = \frac{-7}{6} \\ V = \Big\{ 0 ; \frac{-7}{6} \Big\} \\ -----------------\)
12. \(-2(5x^2+3x)=-(18x^2+31x) \\ \Leftrightarrow -10x^2-6x=-18x^2-31x \\ \Leftrightarrow -10x^2-6x+18x^2+31x= 0 \\ \Leftrightarrow 8x^2-25x=0 \\ \Leftrightarrow x(8x-25) = 0 \\ \Leftrightarrow x = 0 \vee 8x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{8} \\ V = \Big\{ \frac{25}{8}; 0 \Big\} \\ -----------------\)