Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2-2x=0\)
2. \(4(2x^2-8x)=-(-15x^2+54x)\)
3. \(2(10x^2-3x)=-(-23x^2-10x)\)
4. \(-14x^2+15x=-10x^2+2x\)
5. \(-2x^2+2x=-4x^2-3x\)
6. \(-3(7x^2+7x)=-(26x^2+3x)\)
7. \(4(-4x^2+6x)=-(9x^2-9x)\)
8. \(-x^2-4x=0\)
9. \(4x^2-20x=0\)
10. \(-7x^2-4x=0\)
11. \(5(-5x^2+10x)=-(24x^2-30x)\)
12. \(9x^2-16x=7x^2-7x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2-2x=0 \\ \Leftrightarrow x(5x-2) = 0 \\ \Leftrightarrow x = 0 \vee 5x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{5} \\ V = \Big\{ \frac{2}{5}; 0 \Big\} \\ -----------------\)
2. \(4(2x^2-8x)=-(-15x^2+54x) \\ \Leftrightarrow 8x^2-32x=15x^2-54x \\ \Leftrightarrow 8x^2-32x-15x^2+54x= 0 \\ \Leftrightarrow -7x^2-22x=0 \\ \Leftrightarrow x(-7x-22) = 0 \\ \Leftrightarrow x = 0 \vee -7x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-7} = \frac{-22}{7} \\ V = \Big\{ 0 ; \frac{-22}{7} \Big\} \\ -----------------\)
3. \(2(10x^2-3x)=-(-23x^2-10x) \\ \Leftrightarrow 20x^2-6x=23x^2+10x \\ \Leftrightarrow 20x^2-6x-23x^2-10x= 0 \\ \Leftrightarrow -3x^2+16x=0 \\ \Leftrightarrow x(-3x+16) = 0 \\ \Leftrightarrow x = 0 \vee -3x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-3} = \frac{16}{3} \\ V = \Big\{ \frac{16}{3}; 0 \Big\} \\ -----------------\)
4. \(-14x^2+15x=-10x^2+2x \\ \Leftrightarrow -4x^2+13x=0 \\ \Leftrightarrow x(-4x+13) = 0 \\ \Leftrightarrow x = 0 \vee -4x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-4} = \frac{13}{4} \\ V = \Big\{ \frac{13}{4}; 0 \Big\} \\ -----------------\)
5. \(-2x^2+2x=-4x^2-3x \\ \Leftrightarrow 2x^2+5x=0 \\ \Leftrightarrow x(2x+5) = 0 \\ \Leftrightarrow x = 0 \vee 2x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
6. \(-3(7x^2+7x)=-(26x^2+3x) \\ \Leftrightarrow -21x^2-21x=-26x^2-3x \\ \Leftrightarrow -21x^2-21x+26x^2+3x= 0 \\ \Leftrightarrow 5x^2+18x=0 \\ \Leftrightarrow x(5x+18) = 0 \\ \Leftrightarrow x = 0 \vee 5x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{5} \\ V = \Big\{ 0 ; \frac{-18}{5} \Big\} \\ -----------------\)
7. \(4(-4x^2+6x)=-(9x^2-9x) \\ \Leftrightarrow -16x^2+24x=-9x^2+9x \\ \Leftrightarrow -16x^2+24x+9x^2-9x= 0 \\ \Leftrightarrow -7x^2-15x=0 \\ \Leftrightarrow x(-7x-15) = 0 \\ \Leftrightarrow x = 0 \vee -7x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-7} = \frac{-15}{7} \\ V = \Big\{ 0 ; \frac{-15}{7} \Big\} \\ -----------------\)
8. \(-x^2-4x=0 \\ \Leftrightarrow x(-x-4) = 0 \\ \Leftrightarrow x = 0 \vee -x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-1} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
9. \(4x^2-20x=0 \\ \Leftrightarrow x(4x-20) = 0 \\ \Leftrightarrow x = 0 \vee 4x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{4} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
10. \(-7x^2-4x=0 \\ \Leftrightarrow x(-7x-4) = 0 \\ \Leftrightarrow x = 0 \vee -7x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-7} = \frac{-4}{7} \\ V = \Big\{ 0 ; \frac{-4}{7} \Big\} \\ -----------------\)
11. \(5(-5x^2+10x)=-(24x^2-30x) \\ \Leftrightarrow -25x^2+50x=-24x^2+30x \\ \Leftrightarrow -25x^2+50x+24x^2-30x= 0 \\ \Leftrightarrow -x^2-20x=0 \\ \Leftrightarrow x(-x-20) = 0 \\ \Leftrightarrow x = 0 \vee -x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-1} = -20 \\ V = \Big\{ 0 ; -20 \Big\} \\ -----------------\)
12. \(9x^2-16x=7x^2-7x \\ \Leftrightarrow 2x^2-9x=0 \\ \Leftrightarrow x(2x-9) = 0 \\ \Leftrightarrow x = 0 \vee 2x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{2} \\ V = \Big\{ \frac{9}{2}; 0 \Big\} \\ -----------------\)