Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2-8x=0\)
2. \(4x^2+7x=-2x^2-5x\)
3. \(-4(-8x^2-2x)=-(-29x^2-20x)\)
4. \(-3(-9x^2+3x)=-(-23x^2+18x)\)
5. \(2(-3x^2+2x)=-(2x^2+11x)\)
6. \(4(-6x^2-7x)=-(26x^2+20x)\)
7. \(3(7x^2-6x)=-(-13x^2+42x)\)
8. \(2(10x^2+8x)=-(-24x^2-38x)\)
9. \(5x^2-21x=0\)
10. \(x^2-9x=0\)
11. \(13x^2+11x=6x^2+10x\)
12. \(-5(-3x^2+10x)=-(-10x^2+67x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2-8x=0 \\ \Leftrightarrow x(5x-8) = 0 \\ \Leftrightarrow x = 0 \vee 5x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{5} \\ V = \Big\{ \frac{8}{5}; 0 \Big\} \\ -----------------\)
2. \(4x^2+7x=-2x^2-5x \\ \Leftrightarrow 6x^2+12x=0 \\ \Leftrightarrow x(6x+12) = 0 \\ \Leftrightarrow x = 0 \vee 6x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{6} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
3. \(-4(-8x^2-2x)=-(-29x^2-20x) \\ \Leftrightarrow 32x^2+8x=29x^2+20x \\ \Leftrightarrow 32x^2+8x-29x^2-20x= 0 \\ \Leftrightarrow 3x^2+12x=0 \\ \Leftrightarrow x(3x+12) = 0 \\ \Leftrightarrow x = 0 \vee 3x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{3} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
4. \(-3(-9x^2+3x)=-(-23x^2+18x) \\ \Leftrightarrow 27x^2-9x=23x^2-18x \\ \Leftrightarrow 27x^2-9x-23x^2+18x= 0 \\ \Leftrightarrow 4x^2-9x=0 \\ \Leftrightarrow x(4x-9) = 0 \\ \Leftrightarrow x = 0 \vee 4x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
5. \(2(-3x^2+2x)=-(2x^2+11x) \\ \Leftrightarrow -6x^2+4x=-2x^2-11x \\ \Leftrightarrow -6x^2+4x+2x^2+11x= 0 \\ \Leftrightarrow -4x^2-15x=0 \\ \Leftrightarrow x(-4x-15) = 0 \\ \Leftrightarrow x = 0 \vee -4x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-4} = \frac{-15}{4} \\ V = \Big\{ 0 ; \frac{-15}{4} \Big\} \\ -----------------\)
6. \(4(-6x^2-7x)=-(26x^2+20x) \\ \Leftrightarrow -24x^2-28x=-26x^2-20x \\ \Leftrightarrow -24x^2-28x+26x^2+20x= 0 \\ \Leftrightarrow 2x^2+8x=0 \\ \Leftrightarrow x(2x+8) = 0 \\ \Leftrightarrow x = 0 \vee 2x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{2} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
7. \(3(7x^2-6x)=-(-13x^2+42x) \\ \Leftrightarrow 21x^2-18x=13x^2-42x \\ \Leftrightarrow 21x^2-18x-13x^2+42x= 0 \\ \Leftrightarrow 8x^2-24x=0 \\ \Leftrightarrow x(8x-24) = 0 \\ \Leftrightarrow x = 0 \vee 8x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{8} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
8. \(2(10x^2+8x)=-(-24x^2-38x) \\ \Leftrightarrow 20x^2+16x=24x^2+38x \\ \Leftrightarrow 20x^2+16x-24x^2-38x= 0 \\ \Leftrightarrow -4x^2+22x=0 \\ \Leftrightarrow x(-4x+22) = 0 \\ \Leftrightarrow x = 0 \vee -4x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-4} = \frac{11}{2} \\ V = \Big\{ \frac{11}{2}; 0 \Big\} \\ -----------------\)
9. \(5x^2-21x=0 \\ \Leftrightarrow x(5x-21) = 0 \\ \Leftrightarrow x = 0 \vee 5x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{5} \\ V = \Big\{ \frac{21}{5}; 0 \Big\} \\ -----------------\)
10. \(x^2-9x=0 \\ \Leftrightarrow x(x-9) = 0 \\ \Leftrightarrow x = 0 \vee x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{1} = 9 \\ V = \Big\{ 9; 0 \Big\} \\ -----------------\)
11. \(13x^2+11x=6x^2+10x \\ \Leftrightarrow 7x^2+1x=0 \\ \Leftrightarrow x(7x+1) = 0 \\ \Leftrightarrow x = 0 \vee 7x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{7} \\ V = \Big\{ 0 ; \frac{-1}{7} \Big\} \\ -----------------\)
12. \(-5(-3x^2+10x)=-(-10x^2+67x) \\ \Leftrightarrow 15x^2-50x=10x^2-67x \\ \Leftrightarrow 15x^2-50x-10x^2+67x= 0 \\ \Leftrightarrow 5x^2-17x=0 \\ \Leftrightarrow x(5x-17) = 0 \\ \Leftrightarrow x = 0 \vee 5x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{5} \\ V = \Big\{ \frac{17}{5}; 0 \Big\} \\ -----------------\)