Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2+16x=0\)
2. \(-12x^2+15x=-9x^2-5x\)
3. \(-3(-6x^2+10x)=-(-19x^2+16x)\)
4. \(5(-4x^2-10x)=-(12x^2+48x)\)
5. \(-6x^2+28x=-4x^2+6x\)
6. \(-3x^2-23x=-9x^2-5x\)
7. \(-3(4x^2+8x)=-(19x^2+37x)\)
8. \(-4x^2-22x=0\)
9. \(2(-7x^2-10x)=-(22x^2+45x)\)
10. \(11x^2+2x=8x^2-3x\)
11. \(4x^2-25x=10x^2-9x\)
12. \(2(7x^2-10x)=-(-13x^2+24x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2+16x=0 \\ \Leftrightarrow x(4x+16) = 0 \\ \Leftrightarrow x = 0 \vee 4x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{4} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
2. \(-12x^2+15x=-9x^2-5x \\ \Leftrightarrow -3x^2+20x=0 \\ \Leftrightarrow x(-3x+20) = 0 \\ \Leftrightarrow x = 0 \vee -3x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-3} = \frac{20}{3} \\ V = \Big\{ \frac{20}{3}; 0 \Big\} \\ -----------------\)
3. \(-3(-6x^2+10x)=-(-19x^2+16x) \\ \Leftrightarrow 18x^2-30x=19x^2-16x \\ \Leftrightarrow 18x^2-30x-19x^2+16x= 0 \\ \Leftrightarrow -x^2+14x=0 \\ \Leftrightarrow x(-x+14) = 0 \\ \Leftrightarrow x = 0 \vee -x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-1} = 14 \\ V = \Big\{ 14; 0 \Big\} \\ -----------------\)
4. \(5(-4x^2-10x)=-(12x^2+48x) \\ \Leftrightarrow -20x^2-50x=-12x^2-48x \\ \Leftrightarrow -20x^2-50x+12x^2+48x= 0 \\ \Leftrightarrow -8x^2+2x=0 \\ \Leftrightarrow x(-8x+2) = 0 \\ \Leftrightarrow x = 0 \vee -8x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-8} = \frac{1}{4} \\ V = \Big\{ \frac{1}{4}; 0 \Big\} \\ -----------------\)
5. \(-6x^2+28x=-4x^2+6x \\ \Leftrightarrow -2x^2+22x=0 \\ \Leftrightarrow x(-2x+22) = 0 \\ \Leftrightarrow x = 0 \vee -2x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-2} = 11 \\ V = \Big\{ 11; 0 \Big\} \\ -----------------\)
6. \(-3x^2-23x=-9x^2-5x \\ \Leftrightarrow 6x^2-18x=0 \\ \Leftrightarrow x(6x-18) = 0 \\ \Leftrightarrow x = 0 \vee 6x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{6} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
7. \(-3(4x^2+8x)=-(19x^2+37x) \\ \Leftrightarrow -12x^2-24x=-19x^2-37x \\ \Leftrightarrow -12x^2-24x+19x^2+37x= 0 \\ \Leftrightarrow 7x^2-13x=0 \\ \Leftrightarrow x(7x-13) = 0 \\ \Leftrightarrow x = 0 \vee 7x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{7} \\ V = \Big\{ \frac{13}{7}; 0 \Big\} \\ -----------------\)
8. \(-4x^2-22x=0 \\ \Leftrightarrow x(-4x-22) = 0 \\ \Leftrightarrow x = 0 \vee -4x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-4} = \frac{-11}{2} \\ V = \Big\{ 0 ; \frac{-11}{2} \Big\} \\ -----------------\)
9. \(2(-7x^2-10x)=-(22x^2+45x) \\ \Leftrightarrow -14x^2-20x=-22x^2-45x \\ \Leftrightarrow -14x^2-20x+22x^2+45x= 0 \\ \Leftrightarrow 8x^2-25x=0 \\ \Leftrightarrow x(8x-25) = 0 \\ \Leftrightarrow x = 0 \vee 8x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{8} \\ V = \Big\{ \frac{25}{8}; 0 \Big\} \\ -----------------\)
10. \(11x^2+2x=8x^2-3x \\ \Leftrightarrow 3x^2+5x=0 \\ \Leftrightarrow x(3x+5) = 0 \\ \Leftrightarrow x = 0 \vee 3x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{3} \\ V = \Big\{ 0 ; \frac{-5}{3} \Big\} \\ -----------------\)
11. \(4x^2-25x=10x^2-9x \\ \Leftrightarrow -6x^2-16x=0 \\ \Leftrightarrow x(-6x-16) = 0 \\ \Leftrightarrow x = 0 \vee -6x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-6} = \frac{-8}{3} \\ V = \Big\{ 0 ; \frac{-8}{3} \Big\} \\ -----------------\)
12. \(2(7x^2-10x)=-(-13x^2+24x) \\ \Leftrightarrow 14x^2-20x=13x^2-24x \\ \Leftrightarrow 14x^2-20x-13x^2+24x= 0 \\ \Leftrightarrow x^2-4x=0 \\ \Leftrightarrow x(x-4) = 0 \\ \Leftrightarrow x = 0 \vee x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{1} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)