Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(6x^2-3x)=-(-37x^2+3x)\)
2. \(-7x^2+1x=0\)
3. \(-6x^2+15x=0\)
4. \(7x^2+14x=0\)
5. \(-11x^2+34x=-7x^2+10x\)
6. \(8x^2-10x=0\)
7. \(2(4x^2-10x)=-(-16x^2-2x)\)
8. \(-3(-7x^2+5x)=-(-13x^2+x)\)
9. \(-3x^2+3x=0\)
10. \(x^2+0x=0\)
11. \(3(5x^2-8x)=-(-8x^2+46x)\)
12. \(3x^2-10x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(6x^2-3x)=-(-37x^2+3x) \\ \Leftrightarrow 30x^2-15x=37x^2-3x \\ \Leftrightarrow 30x^2-15x-37x^2+3x= 0 \\ \Leftrightarrow -7x^2+12x=0 \\ \Leftrightarrow x(-7x+12) = 0 \\ \Leftrightarrow x = 0 \vee -7x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{-7} = \frac{12}{7} \\ V = \Big\{ \frac{12}{7}; 0 \Big\} \\ -----------------\)
2. \(-7x^2+1x=0 \\ \Leftrightarrow x(-7x+1) = 0 \\ \Leftrightarrow x = 0 \vee -7x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-7} = \frac{1}{7} \\ V = \Big\{ \frac{1}{7}; 0 \Big\} \\ -----------------\)
3. \(-6x^2+15x=0 \\ \Leftrightarrow x(-6x+15) = 0 \\ \Leftrightarrow x = 0 \vee -6x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-6} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
4. \(7x^2+14x=0 \\ \Leftrightarrow x(7x+14) = 0 \\ \Leftrightarrow x = 0 \vee 7x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{7} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
5. \(-11x^2+34x=-7x^2+10x \\ \Leftrightarrow -4x^2+24x=0 \\ \Leftrightarrow x(-4x+24) = 0 \\ \Leftrightarrow x = 0 \vee -4x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-4} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
6. \(8x^2-10x=0 \\ \Leftrightarrow x(8x-10) = 0 \\ \Leftrightarrow x = 0 \vee 8x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{8} = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
7. \(2(4x^2-10x)=-(-16x^2-2x) \\ \Leftrightarrow 8x^2-20x=16x^2+2x \\ \Leftrightarrow 8x^2-20x-16x^2-2x= 0 \\ \Leftrightarrow -8x^2+22x=0 \\ \Leftrightarrow x(-8x+22) = 0 \\ \Leftrightarrow x = 0 \vee -8x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-8} = \frac{11}{4} \\ V = \Big\{ \frac{11}{4}; 0 \Big\} \\ -----------------\)
8. \(-3(-7x^2+5x)=-(-13x^2+x) \\ \Leftrightarrow 21x^2-15x=13x^2-x \\ \Leftrightarrow 21x^2-15x-13x^2+x= 0 \\ \Leftrightarrow 8x^2+14x=0 \\ \Leftrightarrow x(8x+14) = 0 \\ \Leftrightarrow x = 0 \vee 8x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{8} = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)
9. \(-3x^2+3x=0 \\ \Leftrightarrow x(-3x+3) = 0 \\ \Leftrightarrow x = 0 \vee -3x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-3} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
10. \(x^2+0x=0 \\ \Leftrightarrow x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{1} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(3(5x^2-8x)=-(-8x^2+46x) \\ \Leftrightarrow 15x^2-24x=8x^2-46x \\ \Leftrightarrow 15x^2-24x-8x^2+46x= 0 \\ \Leftrightarrow 7x^2-22x=0 \\ \Leftrightarrow x(7x-22) = 0 \\ \Leftrightarrow x = 0 \vee 7x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{7} \\ V = \Big\{ \frac{22}{7}; 0 \Big\} \\ -----------------\)
12. \(3x^2-10x=0 \\ \Leftrightarrow x(3x-10) = 0 \\ \Leftrightarrow x = 0 \vee 3x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)