Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(5x^2+3x)=-(13x^2-7x)\)
2. \(-4x^2+22x=0\)
3. \(x^2+13x=0\)
4. \(-8x^2-2x=0\)
5. \(7x^2-21x=0\)
6. \(5x^2+6x=9x^2+7x\)
7. \(-5x^2+8x=3x^2-2x\)
8. \(-3x^2-16x=-5x^2+2x\)
9. \(4x^2+11x=0\)
10. \(3x^2+12x=0\)
11. \(-7x^2-11x=-4x^2-5x\)
12. \(-12x^2+x=-5x^2+8x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

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