Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(-10x^2+8x)=-(-27x^2+29x)\)
2. \(4x^2-13x=0\)
3. \(5(2x^2+4x)=-(-18x^2-29x)\)
4. \(7x^2+22x=0\)
5. \(4(-9x^2+7x)=-(34x^2-14x)\)
6. \(-2(7x^2-9x)=-(8x^2-29x)\)
7. \(8x^2+2x=0\)
8. \(8x^2+21x=0\)
9. \(5x^2+11x=6x^2-6x\)
10. \(-3x^2-2x=0\)
11. \(-3(-10x^2+2x)=-(-34x^2+10x)\)
12. \(-2x^2+23x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(-10x^2+8x)=-(-27x^2+29x) \\ \Leftrightarrow 30x^2-24x=27x^2-29x \\ \Leftrightarrow 30x^2-24x-27x^2+29x= 0 \\ \Leftrightarrow 3x^2-5x=0 \\ \Leftrightarrow x(3x-5) = 0 \\ \Leftrightarrow x = 0 \vee 3x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{3} \\ V = \Big\{ \frac{5}{3}; 0 \Big\} \\ -----------------\)
2. \(4x^2-13x=0 \\ \Leftrightarrow x(4x-13) = 0 \\ \Leftrightarrow x = 0 \vee 4x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{4} \\ V = \Big\{ \frac{13}{4}; 0 \Big\} \\ -----------------\)
3. \(5(2x^2+4x)=-(-18x^2-29x) \\ \Leftrightarrow 10x^2+20x=18x^2+29x \\ \Leftrightarrow 10x^2+20x-18x^2-29x= 0 \\ \Leftrightarrow -8x^2+9x=0 \\ \Leftrightarrow x(-8x+9) = 0 \\ \Leftrightarrow x = 0 \vee -8x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-8} = \frac{9}{8} \\ V = \Big\{ \frac{9}{8}; 0 \Big\} \\ -----------------\)
4. \(7x^2+22x=0 \\ \Leftrightarrow x(7x+22) = 0 \\ \Leftrightarrow x = 0 \vee 7x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{7} \\ V = \Big\{ 0 ; \frac{-22}{7} \Big\} \\ -----------------\)
5. \(4(-9x^2+7x)=-(34x^2-14x) \\ \Leftrightarrow -36x^2+28x=-34x^2+14x \\ \Leftrightarrow -36x^2+28x+34x^2-14x= 0 \\ \Leftrightarrow -2x^2-14x=0 \\ \Leftrightarrow x(-2x-14) = 0 \\ \Leftrightarrow x = 0 \vee -2x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-2} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)
6. \(-2(7x^2-9x)=-(8x^2-29x) \\ \Leftrightarrow -14x^2+18x=-8x^2+29x \\ \Leftrightarrow -14x^2+18x+8x^2-29x= 0 \\ \Leftrightarrow -6x^2+11x=0 \\ \Leftrightarrow x(-6x+11) = 0 \\ \Leftrightarrow x = 0 \vee -6x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-6} = \frac{11}{6} \\ V = \Big\{ \frac{11}{6}; 0 \Big\} \\ -----------------\)
7. \(8x^2+2x=0 \\ \Leftrightarrow x(8x+2) = 0 \\ \Leftrightarrow x = 0 \vee 8x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{8} = \frac{-1}{4} \\ V = \Big\{ 0 ; \frac{-1}{4} \Big\} \\ -----------------\)
8. \(8x^2+21x=0 \\ \Leftrightarrow x(8x+21) = 0 \\ \Leftrightarrow x = 0 \vee 8x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{8} \\ V = \Big\{ 0 ; \frac{-21}{8} \Big\} \\ -----------------\)
9. \(5x^2+11x=6x^2-6x \\ \Leftrightarrow -x^2+17x=0 \\ \Leftrightarrow x(-x+17) = 0 \\ \Leftrightarrow x = 0 \vee -x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-1} = 17 \\ V = \Big\{ 17; 0 \Big\} \\ -----------------\)
10. \(-3x^2-2x=0 \\ \Leftrightarrow x(-3x-2) = 0 \\ \Leftrightarrow x = 0 \vee -3x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-3} = \frac{-2}{3} \\ V = \Big\{ 0 ; \frac{-2}{3} \Big\} \\ -----------------\)
11. \(-3(-10x^2+2x)=-(-34x^2+10x) \\ \Leftrightarrow 30x^2-6x=34x^2-10x \\ \Leftrightarrow 30x^2-6x-34x^2+10x= 0 \\ \Leftrightarrow -4x^2-4x=0 \\ \Leftrightarrow x(-4x-4) = 0 \\ \Leftrightarrow x = 0 \vee -4x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-4} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
12. \(-2x^2+23x=0 \\ \Leftrightarrow x(-2x+23) = 0 \\ \Leftrightarrow x = 0 \vee -2x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-2} = \frac{23}{2} \\ V = \Big\{ \frac{23}{2}; 0 \Big\} \\ -----------------\)