Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-11x^2+3x=-6x^2+8x\)
2. \(2x^2-21x=0\)
3. \(8x^2+20x=0\)
4. \(16x^2+29x=9x^2+8x\)
5. \(-x^2-14x=0\)
6. \(-3(-6x^2-2x)=-(-21x^2-3x)\)
7. \(4(3x^2-3x)=-(-18x^2+27x)\)
8. \(-4(10x^2-10x)=-(41x^2-20x)\)
9. \(5(4x^2-4x)=-(-28x^2+28x)\)
10. \(4(-3x^2-5x)=-(6x^2+32x)\)
11. \(-5x^2-20x=0\)
12. \(3(-3x^2+2x)=-(7x^2+4x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-11x^2+3x=-6x^2+8x \\ \Leftrightarrow -5x^2-5x=0 \\ \Leftrightarrow x(-5x-5) = 0 \\ \Leftrightarrow x = 0 \vee -5x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-5} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
2. \(2x^2-21x=0 \\ \Leftrightarrow x(2x-21) = 0 \\ \Leftrightarrow x = 0 \vee 2x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{2} \\ V = \Big\{ \frac{21}{2}; 0 \Big\} \\ -----------------\)
3. \(8x^2+20x=0 \\ \Leftrightarrow x(8x+20) = 0 \\ \Leftrightarrow x = 0 \vee 8x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{8} = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
4. \(16x^2+29x=9x^2+8x \\ \Leftrightarrow 7x^2+21x=0 \\ \Leftrightarrow x(7x+21) = 0 \\ \Leftrightarrow x = 0 \vee 7x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{7} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
5. \(-x^2-14x=0 \\ \Leftrightarrow x(-x-14) = 0 \\ \Leftrightarrow x = 0 \vee -x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-1} = -14 \\ V = \Big\{ 0 ; -14 \Big\} \\ -----------------\)
6. \(-3(-6x^2-2x)=-(-21x^2-3x) \\ \Leftrightarrow 18x^2+6x=21x^2+3x \\ \Leftrightarrow 18x^2+6x-21x^2-3x= 0 \\ \Leftrightarrow -3x^2-3x=0 \\ \Leftrightarrow x(-3x-3) = 0 \\ \Leftrightarrow x = 0 \vee -3x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-3} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
7. \(4(3x^2-3x)=-(-18x^2+27x) \\ \Leftrightarrow 12x^2-12x=18x^2-27x \\ \Leftrightarrow 12x^2-12x-18x^2+27x= 0 \\ \Leftrightarrow -6x^2-15x=0 \\ \Leftrightarrow x(-6x-15) = 0 \\ \Leftrightarrow x = 0 \vee -6x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-6} = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
8. \(-4(10x^2-10x)=-(41x^2-20x) \\ \Leftrightarrow -40x^2+40x=-41x^2+20x \\ \Leftrightarrow -40x^2+40x+41x^2-20x= 0 \\ \Leftrightarrow x^2-20x=0 \\ \Leftrightarrow x(x-20) = 0 \\ \Leftrightarrow x = 0 \vee x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{1} = 20 \\ V = \Big\{ 20; 0 \Big\} \\ -----------------\)
9. \(5(4x^2-4x)=-(-28x^2+28x) \\ \Leftrightarrow 20x^2-20x=28x^2-28x \\ \Leftrightarrow 20x^2-20x-28x^2+28x= 0 \\ \Leftrightarrow -8x^2-8x=0 \\ \Leftrightarrow x(-8x-8) = 0 \\ \Leftrightarrow x = 0 \vee -8x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-8} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
10. \(4(-3x^2-5x)=-(6x^2+32x) \\ \Leftrightarrow -12x^2-20x=-6x^2-32x \\ \Leftrightarrow -12x^2-20x+6x^2+32x= 0 \\ \Leftrightarrow -6x^2-12x=0 \\ \Leftrightarrow x(-6x-12) = 0 \\ \Leftrightarrow x = 0 \vee -6x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-6} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
11. \(-5x^2-20x=0 \\ \Leftrightarrow x(-5x-20) = 0 \\ \Leftrightarrow x = 0 \vee -5x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-5} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
12. \(3(-3x^2+2x)=-(7x^2+4x) \\ \Leftrightarrow -9x^2+6x=-7x^2-4x \\ \Leftrightarrow -9x^2+6x+7x^2+4x= 0 \\ \Leftrightarrow -2x^2-10x=0 \\ \Leftrightarrow x(-2x-10) = 0 \\ \Leftrightarrow x = 0 \vee -2x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-2} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)