Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(6x^2-6x=0\)
2. \(13x^2-x=7x^2-8x\)
3. \(-6x^2-15x=-5x^2-8x\)
4. \(-3(9x^2-10x)=-(32x^2-30x)\)
5. \(8x^2-17x=0\)
6. \(-5(4x^2-2x)=-(17x^2-29x)\)
7. \(4(6x^2-9x)=-(-27x^2+28x)\)
8. \(x^2-25x=3x^2-9x\)
9. \(-2(-4x^2-3x)=-(-15x^2+18x)\)
10. \(4(9x^2+4x)=-(-39x^2-13x)\)
11. \(-3x^2-17x=-8x^2-8x\)
12. \(-5x^2-5x=-2x^2+7x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(6x^2-6x=0 \\ \Leftrightarrow x(6x-6) = 0 \\ \Leftrightarrow x = 0 \vee 6x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{6} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
2. \(13x^2-x=7x^2-8x \\ \Leftrightarrow 6x^2+7x=0 \\ \Leftrightarrow x(6x+7) = 0 \\ \Leftrightarrow x = 0 \vee 6x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{6} \\ V = \Big\{ 0 ; \frac{-7}{6} \Big\} \\ -----------------\)
3. \(-6x^2-15x=-5x^2-8x \\ \Leftrightarrow -x^2-7x=0 \\ \Leftrightarrow x(-x-7) = 0 \\ \Leftrightarrow x = 0 \vee -x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-1} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)
4. \(-3(9x^2-10x)=-(32x^2-30x) \\ \Leftrightarrow -27x^2+30x=-32x^2+30x \\ \Leftrightarrow -27x^2+30x+32x^2-30x= 0 \\ \Leftrightarrow 5x^2+0x=0 \\ \Leftrightarrow 5x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{5} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(8x^2-17x=0 \\ \Leftrightarrow x(8x-17) = 0 \\ \Leftrightarrow x = 0 \vee 8x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{8} \\ V = \Big\{ \frac{17}{8}; 0 \Big\} \\ -----------------\)
6. \(-5(4x^2-2x)=-(17x^2-29x) \\ \Leftrightarrow -20x^2+10x=-17x^2+29x \\ \Leftrightarrow -20x^2+10x+17x^2-29x= 0 \\ \Leftrightarrow -3x^2+19x=0 \\ \Leftrightarrow x(-3x+19) = 0 \\ \Leftrightarrow x = 0 \vee -3x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-3} = \frac{19}{3} \\ V = \Big\{ \frac{19}{3}; 0 \Big\} \\ -----------------\)
7. \(4(6x^2-9x)=-(-27x^2+28x) \\ \Leftrightarrow 24x^2-36x=27x^2-28x \\ \Leftrightarrow 24x^2-36x-27x^2+28x= 0 \\ \Leftrightarrow -3x^2+8x=0 \\ \Leftrightarrow x(-3x+8) = 0 \\ \Leftrightarrow x = 0 \vee -3x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-3} = \frac{8}{3} \\ V = \Big\{ \frac{8}{3}; 0 \Big\} \\ -----------------\)
8. \(x^2-25x=3x^2-9x \\ \Leftrightarrow -2x^2-16x=0 \\ \Leftrightarrow x(-2x-16) = 0 \\ \Leftrightarrow x = 0 \vee -2x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-2} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
9. \(-2(-4x^2-3x)=-(-15x^2+18x) \\ \Leftrightarrow 8x^2+6x=15x^2-18x \\ \Leftrightarrow 8x^2+6x-15x^2+18x= 0 \\ \Leftrightarrow -7x^2-24x=0 \\ \Leftrightarrow x(-7x-24) = 0 \\ \Leftrightarrow x = 0 \vee -7x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-7} = \frac{-24}{7} \\ V = \Big\{ 0 ; \frac{-24}{7} \Big\} \\ -----------------\)
10. \(4(9x^2+4x)=-(-39x^2-13x) \\ \Leftrightarrow 36x^2+16x=39x^2+13x \\ \Leftrightarrow 36x^2+16x-39x^2-13x= 0 \\ \Leftrightarrow -3x^2-3x=0 \\ \Leftrightarrow x(-3x-3) = 0 \\ \Leftrightarrow x = 0 \vee -3x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-3} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
11. \(-3x^2-17x=-8x^2-8x \\ \Leftrightarrow 5x^2-9x=0 \\ \Leftrightarrow x(5x-9) = 0 \\ \Leftrightarrow x = 0 \vee 5x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{5} \\ V = \Big\{ \frac{9}{5}; 0 \Big\} \\ -----------------\)
12. \(-5x^2-5x=-2x^2+7x \\ \Leftrightarrow -3x^2-12x=0 \\ \Leftrightarrow x(-3x-12) = 0 \\ \Leftrightarrow x = 0 \vee -3x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-3} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)