Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(10x^2+14x=4x^2-2x\)
2. \(-2(5x^2-7x)=-(6x^2-23x)\)
3. \(-5x^2+23x=0\)
4. \(4x^2-3x=0\)
5. \(10x^2-13x=7x^2-10x\)
6. \(3(-2x^2-3x)=-(13x^2+16x)\)
7. \(-5x^2+2x=0\)
8. \(-6x^2-6x=0\)
9. \(-6x^2-5x=0\)
10. \(-9x^2+4x=-5x^2+6x\)
11. \(4x^2-13x=0\)
12. \(3(5x^2-8x)=-(-7x^2+3x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(10x^2+14x=4x^2-2x \\ \Leftrightarrow 6x^2+16x=0 \\ \Leftrightarrow x(6x+16) = 0 \\ \Leftrightarrow x = 0 \vee 6x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{6} = \frac{-8}{3} \\ V = \Big\{ 0 ; \frac{-8}{3} \Big\} \\ -----------------\)
2. \(-2(5x^2-7x)=-(6x^2-23x) \\ \Leftrightarrow -10x^2+14x=-6x^2+23x \\ \Leftrightarrow -10x^2+14x+6x^2-23x= 0 \\ \Leftrightarrow -4x^2+9x=0 \\ \Leftrightarrow x(-4x+9) = 0 \\ \Leftrightarrow x = 0 \vee -4x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-4} = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
3. \(-5x^2+23x=0 \\ \Leftrightarrow x(-5x+23) = 0 \\ \Leftrightarrow x = 0 \vee -5x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-5} = \frac{23}{5} \\ V = \Big\{ \frac{23}{5}; 0 \Big\} \\ -----------------\)
4. \(4x^2-3x=0 \\ \Leftrightarrow x(4x-3) = 0 \\ \Leftrightarrow x = 0 \vee 4x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{4} \\ V = \Big\{ \frac{3}{4}; 0 \Big\} \\ -----------------\)
5. \(10x^2-13x=7x^2-10x \\ \Leftrightarrow 3x^2-3x=0 \\ \Leftrightarrow x(3x-3) = 0 \\ \Leftrightarrow x = 0 \vee 3x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{3} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
6. \(3(-2x^2-3x)=-(13x^2+16x) \\ \Leftrightarrow -6x^2-9x=-13x^2-16x \\ \Leftrightarrow -6x^2-9x+13x^2+16x= 0 \\ \Leftrightarrow 7x^2-7x=0 \\ \Leftrightarrow x(7x-7) = 0 \\ \Leftrightarrow x = 0 \vee 7x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{7} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
7. \(-5x^2+2x=0 \\ \Leftrightarrow x(-5x+2) = 0 \\ \Leftrightarrow x = 0 \vee -5x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-5} = \frac{2}{5} \\ V = \Big\{ \frac{2}{5}; 0 \Big\} \\ -----------------\)
8. \(-6x^2-6x=0 \\ \Leftrightarrow x(-6x-6) = 0 \\ \Leftrightarrow x = 0 \vee -6x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-6} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
9. \(-6x^2-5x=0 \\ \Leftrightarrow x(-6x-5) = 0 \\ \Leftrightarrow x = 0 \vee -6x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-6} = \frac{-5}{6} \\ V = \Big\{ 0 ; \frac{-5}{6} \Big\} \\ -----------------\)
10. \(-9x^2+4x=-5x^2+6x \\ \Leftrightarrow -4x^2-2x=0 \\ \Leftrightarrow x(-4x-2) = 0 \\ \Leftrightarrow x = 0 \vee -4x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-4} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
11. \(4x^2-13x=0 \\ \Leftrightarrow x(4x-13) = 0 \\ \Leftrightarrow x = 0 \vee 4x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{4} \\ V = \Big\{ \frac{13}{4}; 0 \Big\} \\ -----------------\)
12. \(3(5x^2-8x)=-(-7x^2+3x) \\ \Leftrightarrow 15x^2-24x=7x^2-3x \\ \Leftrightarrow 15x^2-24x-7x^2+3x= 0 \\ \Leftrightarrow 8x^2+21x=0 \\ \Leftrightarrow x(8x+21) = 0 \\ \Leftrightarrow x = 0 \vee 8x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{8} \\ V = \Big\{ 0 ; \frac{-21}{8} \Big\} \\ -----------------\)