Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(9x^2+12x=8x^2+5x\)
2. \(2(-3x^2-3x)=-(4x^2-14x)\)
3. \(4x^2+4x=0\)
4. \(5(9x^2-3x)=-(-53x^2-8x)\)
5. \(-x^2+25x=0\)
6. \(-3(4x^2-2x)=-(19x^2+3x)\)
7. \(3x^2-19x=0\)
8. \(-6x^2-9x=0\)
9. \(-2(-10x^2+7x)=-(-24x^2+9x)\)
10. \(-8x^2-17x=-7x^2+4x\)
11. \(-3x^2+11x=3x^2-4x\)
12. \(-7x^2+6x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(9x^2+12x=8x^2+5x \\ \Leftrightarrow x^2+7x=0 \\ \Leftrightarrow x(x+7) = 0 \\ \Leftrightarrow x = 0 \vee x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{1} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)
2. \(2(-3x^2-3x)=-(4x^2-14x) \\ \Leftrightarrow -6x^2-6x=-4x^2+14x \\ \Leftrightarrow -6x^2-6x+4x^2-14x= 0 \\ \Leftrightarrow -2x^2+20x=0 \\ \Leftrightarrow x(-2x+20) = 0 \\ \Leftrightarrow x = 0 \vee -2x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-2} = 10 \\ V = \Big\{ 10; 0 \Big\} \\ -----------------\)
3. \(4x^2+4x=0 \\ \Leftrightarrow x(4x+4) = 0 \\ \Leftrightarrow x = 0 \vee 4x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{4} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
4. \(5(9x^2-3x)=-(-53x^2-8x) \\ \Leftrightarrow 45x^2-15x=53x^2+8x \\ \Leftrightarrow 45x^2-15x-53x^2-8x= 0 \\ \Leftrightarrow -8x^2+23x=0 \\ \Leftrightarrow x(-8x+23) = 0 \\ \Leftrightarrow x = 0 \vee -8x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-8} = \frac{23}{8} \\ V = \Big\{ \frac{23}{8}; 0 \Big\} \\ -----------------\)
5. \(-x^2+25x=0 \\ \Leftrightarrow x(-x+25) = 0 \\ \Leftrightarrow x = 0 \vee -x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-1} = 25 \\ V = \Big\{ 25; 0 \Big\} \\ -----------------\)
6. \(-3(4x^2-2x)=-(19x^2+3x) \\ \Leftrightarrow -12x^2+6x=-19x^2-3x \\ \Leftrightarrow -12x^2+6x+19x^2+3x= 0 \\ \Leftrightarrow 7x^2-9x=0 \\ \Leftrightarrow x(7x-9) = 0 \\ \Leftrightarrow x = 0 \vee 7x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{7} \\ V = \Big\{ \frac{9}{7}; 0 \Big\} \\ -----------------\)
7. \(3x^2-19x=0 \\ \Leftrightarrow x(3x-19) = 0 \\ \Leftrightarrow x = 0 \vee 3x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{3} \\ V = \Big\{ \frac{19}{3}; 0 \Big\} \\ -----------------\)
8. \(-6x^2-9x=0 \\ \Leftrightarrow x(-6x-9) = 0 \\ \Leftrightarrow x = 0 \vee -6x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-6} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
9. \(-2(-10x^2+7x)=-(-24x^2+9x) \\ \Leftrightarrow 20x^2-14x=24x^2-9x \\ \Leftrightarrow 20x^2-14x-24x^2+9x= 0 \\ \Leftrightarrow -4x^2+5x=0 \\ \Leftrightarrow x(-4x+5) = 0 \\ \Leftrightarrow x = 0 \vee -4x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-4} = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
10. \(-8x^2-17x=-7x^2+4x \\ \Leftrightarrow -x^2-21x=0 \\ \Leftrightarrow x(-x-21) = 0 \\ \Leftrightarrow x = 0 \vee -x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-1} = -21 \\ V = \Big\{ 0 ; -21 \Big\} \\ -----------------\)
11. \(-3x^2+11x=3x^2-4x \\ \Leftrightarrow -6x^2+15x=0 \\ \Leftrightarrow x(-6x+15) = 0 \\ \Leftrightarrow x = 0 \vee -6x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-6} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
12. \(-7x^2+6x=0 \\ \Leftrightarrow x(-7x+6) = 0 \\ \Leftrightarrow x = 0 \vee -7x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-7} = \frac{6}{7} \\ V = \Big\{ \frac{6}{7}; 0 \Big\} \\ -----------------\)