Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+15x=0\)
2. \(4(-4x^2-3x)=-(17x^2+19x)\)
3. \(-4(-2x^2-8x)=-(-14x^2-51x)\)
4. \(-2x^2+29x=3x^2+8x\)
5. \(-3(-8x^2-7x)=-(-26x^2-26x)\)
6. \(3x^2-7x=-2x^2+7x\)
7. \(4x^2-7x=3x^2+2x\)
8. \(2x^2+13x=-2x^2+4x\)
9. \(-3x^2-25x=0\)
10. \(4(-2x^2+8x)=-(13x^2-43x)\)
11. \(-4x^2+31x=-8x^2+10x\)
12. \(4(5x^2+2x)=-(-16x^2-13x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+15x=0 \\ \Leftrightarrow x(-4x+15) = 0 \\ \Leftrightarrow x = 0 \vee -4x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-4} = \frac{15}{4} \\ V = \Big\{ \frac{15}{4}; 0 \Big\} \\ -----------------\)
2. \(4(-4x^2-3x)=-(17x^2+19x) \\ \Leftrightarrow -16x^2-12x=-17x^2-19x \\ \Leftrightarrow -16x^2-12x+17x^2+19x= 0 \\ \Leftrightarrow x^2-7x=0 \\ \Leftrightarrow x(x-7) = 0 \\ \Leftrightarrow x = 0 \vee x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{1} = 7 \\ V = \Big\{ 7; 0 \Big\} \\ -----------------\)
3. \(-4(-2x^2-8x)=-(-14x^2-51x) \\ \Leftrightarrow 8x^2+32x=14x^2+51x \\ \Leftrightarrow 8x^2+32x-14x^2-51x= 0 \\ \Leftrightarrow -6x^2+19x=0 \\ \Leftrightarrow x(-6x+19) = 0 \\ \Leftrightarrow x = 0 \vee -6x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-6} = \frac{19}{6} \\ V = \Big\{ \frac{19}{6}; 0 \Big\} \\ -----------------\)
4. \(-2x^2+29x=3x^2+8x \\ \Leftrightarrow -5x^2+21x=0 \\ \Leftrightarrow x(-5x+21) = 0 \\ \Leftrightarrow x = 0 \vee -5x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-5} = \frac{21}{5} \\ V = \Big\{ \frac{21}{5}; 0 \Big\} \\ -----------------\)
5. \(-3(-8x^2-7x)=-(-26x^2-26x) \\ \Leftrightarrow 24x^2+21x=26x^2+26x \\ \Leftrightarrow 24x^2+21x-26x^2-26x= 0 \\ \Leftrightarrow -2x^2+5x=0 \\ \Leftrightarrow x(-2x+5) = 0 \\ \Leftrightarrow x = 0 \vee -2x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-2} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
6. \(3x^2-7x=-2x^2+7x \\ \Leftrightarrow 5x^2-14x=0 \\ \Leftrightarrow x(5x-14) = 0 \\ \Leftrightarrow x = 0 \vee 5x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{5} \\ V = \Big\{ \frac{14}{5}; 0 \Big\} \\ -----------------\)
7. \(4x^2-7x=3x^2+2x \\ \Leftrightarrow x^2-9x=0 \\ \Leftrightarrow x(x-9) = 0 \\ \Leftrightarrow x = 0 \vee x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{1} = 9 \\ V = \Big\{ 9; 0 \Big\} \\ -----------------\)
8. \(2x^2+13x=-2x^2+4x \\ \Leftrightarrow 4x^2+9x=0 \\ \Leftrightarrow x(4x+9) = 0 \\ \Leftrightarrow x = 0 \vee 4x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{4} \\ V = \Big\{ 0 ; \frac{-9}{4} \Big\} \\ -----------------\)
9. \(-3x^2-25x=0 \\ \Leftrightarrow x(-3x-25) = 0 \\ \Leftrightarrow x = 0 \vee -3x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-3} = \frac{-25}{3} \\ V = \Big\{ 0 ; \frac{-25}{3} \Big\} \\ -----------------\)
10. \(4(-2x^2+8x)=-(13x^2-43x) \\ \Leftrightarrow -8x^2+32x=-13x^2+43x \\ \Leftrightarrow -8x^2+32x+13x^2-43x= 0 \\ \Leftrightarrow 5x^2+11x=0 \\ \Leftrightarrow x(5x+11) = 0 \\ \Leftrightarrow x = 0 \vee 5x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{5} \\ V = \Big\{ 0 ; \frac{-11}{5} \Big\} \\ -----------------\)
11. \(-4x^2+31x=-8x^2+10x \\ \Leftrightarrow 4x^2+21x=0 \\ \Leftrightarrow x(4x+21) = 0 \\ \Leftrightarrow x = 0 \vee 4x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{4} \\ V = \Big\{ 0 ; \frac{-21}{4} \Big\} \\ -----------------\)
12. \(4(5x^2+2x)=-(-16x^2-13x) \\ \Leftrightarrow 20x^2+8x=16x^2+13x \\ \Leftrightarrow 20x^2+8x-16x^2-13x= 0 \\ \Leftrightarrow 4x^2+5x=0 \\ \Leftrightarrow x(4x+5) = 0 \\ \Leftrightarrow x = 0 \vee 4x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)