Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2-13x=0\)
2. \(-3x^2+11x=0\)
3. \(2x^2+0x=0\)
4. \(5(-2x^2-7x)=-(15x^2+17x)\)
5. \(-13x^2-31x=-10x^2-10x\)
6. \(5(8x^2-6x)=-(-47x^2+42x)\)
7. \(2(-5x^2+5x)=-(3x^2-2x)\)
8. \(5x^2-18x=9x^2+3x\)
9. \(-3(-5x^2+5x)=-(-16x^2-2x)\)
10. \(8x^2+22x=5x^2+6x\)
11. \(x^2-3x=0\)
12. \(-5(-7x^2+7x)=-(-40x^2+30x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2-13x=0 \\ \Leftrightarrow x(x-13) = 0 \\ \Leftrightarrow x = 0 \vee x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{1} = 13 \\ V = \Big\{ 13; 0 \Big\} \\ -----------------\)
2. \(-3x^2+11x=0 \\ \Leftrightarrow x(-3x+11) = 0 \\ \Leftrightarrow x = 0 \vee -3x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-3} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
3. \(2x^2+0x=0 \\ \Leftrightarrow 2x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{2} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(5(-2x^2-7x)=-(15x^2+17x) \\ \Leftrightarrow -10x^2-35x=-15x^2-17x \\ \Leftrightarrow -10x^2-35x+15x^2+17x= 0 \\ \Leftrightarrow 5x^2+18x=0 \\ \Leftrightarrow x(5x+18) = 0 \\ \Leftrightarrow x = 0 \vee 5x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{5} \\ V = \Big\{ 0 ; \frac{-18}{5} \Big\} \\ -----------------\)
5. \(-13x^2-31x=-10x^2-10x \\ \Leftrightarrow -3x^2-21x=0 \\ \Leftrightarrow x(-3x-21) = 0 \\ \Leftrightarrow x = 0 \vee -3x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-3} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)
6. \(5(8x^2-6x)=-(-47x^2+42x) \\ \Leftrightarrow 40x^2-30x=47x^2-42x \\ \Leftrightarrow 40x^2-30x-47x^2+42x= 0 \\ \Leftrightarrow -7x^2-12x=0 \\ \Leftrightarrow x(-7x-12) = 0 \\ \Leftrightarrow x = 0 \vee -7x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-7} = \frac{-12}{7} \\ V = \Big\{ 0 ; \frac{-12}{7} \Big\} \\ -----------------\)
7. \(2(-5x^2+5x)=-(3x^2-2x) \\ \Leftrightarrow -10x^2+10x=-3x^2+2x \\ \Leftrightarrow -10x^2+10x+3x^2-2x= 0 \\ \Leftrightarrow -7x^2-8x=0 \\ \Leftrightarrow x(-7x-8) = 0 \\ \Leftrightarrow x = 0 \vee -7x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-7} = \frac{-8}{7} \\ V = \Big\{ 0 ; \frac{-8}{7} \Big\} \\ -----------------\)
8. \(5x^2-18x=9x^2+3x \\ \Leftrightarrow -4x^2-21x=0 \\ \Leftrightarrow x(-4x-21) = 0 \\ \Leftrightarrow x = 0 \vee -4x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-4} = \frac{-21}{4} \\ V = \Big\{ 0 ; \frac{-21}{4} \Big\} \\ -----------------\)
9. \(-3(-5x^2+5x)=-(-16x^2-2x) \\ \Leftrightarrow 15x^2-15x=16x^2+2x \\ \Leftrightarrow 15x^2-15x-16x^2-2x= 0 \\ \Leftrightarrow -x^2+17x=0 \\ \Leftrightarrow x(-x+17) = 0 \\ \Leftrightarrow x = 0 \vee -x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-1} = 17 \\ V = \Big\{ 17; 0 \Big\} \\ -----------------\)
10. \(8x^2+22x=5x^2+6x \\ \Leftrightarrow 3x^2+16x=0 \\ \Leftrightarrow x(3x+16) = 0 \\ \Leftrightarrow x = 0 \vee 3x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{3} \\ V = \Big\{ 0 ; \frac{-16}{3} \Big\} \\ -----------------\)
11. \(x^2-3x=0 \\ \Leftrightarrow x(x-3) = 0 \\ \Leftrightarrow x = 0 \vee x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{1} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
12. \(-5(-7x^2+7x)=-(-40x^2+30x) \\ \Leftrightarrow 35x^2-35x=40x^2-30x \\ \Leftrightarrow 35x^2-35x-40x^2+30x= 0 \\ \Leftrightarrow -5x^2+5x=0 \\ \Leftrightarrow x(-5x+5) = 0 \\ \Leftrightarrow x = 0 \vee -5x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-5} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)