Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2-12x=0\)
2. \(-2(-6x^2-2x)=-(-7x^2+5x)\)
3. \(7x^2-14x=4x^2-5x\)
4. \(-3x^2-6x=0\)
5. \(4x^2-9x=5x^2-2x\)
6. \(-3x^2-12x=-7x^2+3x\)
7. \(2(-7x^2+6x)=-(6x^2+2x)\)
8. \(-2x^2+25x=-5x^2+6x\)
9. \(-9x^2+30x=-3x^2+6x\)
10. \(3x^2-24x=0\)
11. \(3(5x^2+2x)=-(-21x^2+16x)\)
12. \(2(2x^2-3x)=-(-12x^2+12x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2-12x=0 \\ \Leftrightarrow x(-8x-12) = 0 \\ \Leftrightarrow x = 0 \vee -8x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-8} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
2. \(-2(-6x^2-2x)=-(-7x^2+5x) \\ \Leftrightarrow 12x^2+4x=7x^2-5x \\ \Leftrightarrow 12x^2+4x-7x^2+5x= 0 \\ \Leftrightarrow 5x^2-9x=0 \\ \Leftrightarrow x(5x-9) = 0 \\ \Leftrightarrow x = 0 \vee 5x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{5} \\ V = \Big\{ \frac{9}{5}; 0 \Big\} \\ -----------------\)
3. \(7x^2-14x=4x^2-5x \\ \Leftrightarrow 3x^2-9x=0 \\ \Leftrightarrow x(3x-9) = 0 \\ \Leftrightarrow x = 0 \vee 3x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{3} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
4. \(-3x^2-6x=0 \\ \Leftrightarrow x(-3x-6) = 0 \\ \Leftrightarrow x = 0 \vee -3x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-3} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
5. \(4x^2-9x=5x^2-2x \\ \Leftrightarrow -x^2-7x=0 \\ \Leftrightarrow x(-x-7) = 0 \\ \Leftrightarrow x = 0 \vee -x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-1} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)
6. \(-3x^2-12x=-7x^2+3x \\ \Leftrightarrow 4x^2-15x=0 \\ \Leftrightarrow x(4x-15) = 0 \\ \Leftrightarrow x = 0 \vee 4x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{4} \\ V = \Big\{ \frac{15}{4}; 0 \Big\} \\ -----------------\)
7. \(2(-7x^2+6x)=-(6x^2+2x) \\ \Leftrightarrow -14x^2+12x=-6x^2-2x \\ \Leftrightarrow -14x^2+12x+6x^2+2x= 0 \\ \Leftrightarrow -8x^2-14x=0 \\ \Leftrightarrow x(-8x-14) = 0 \\ \Leftrightarrow x = 0 \vee -8x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-8} = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)
8. \(-2x^2+25x=-5x^2+6x \\ \Leftrightarrow 3x^2+19x=0 \\ \Leftrightarrow x(3x+19) = 0 \\ \Leftrightarrow x = 0 \vee 3x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{3} \\ V = \Big\{ 0 ; \frac{-19}{3} \Big\} \\ -----------------\)
9. \(-9x^2+30x=-3x^2+6x \\ \Leftrightarrow -6x^2+24x=0 \\ \Leftrightarrow x(-6x+24) = 0 \\ \Leftrightarrow x = 0 \vee -6x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-6} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
10. \(3x^2-24x=0 \\ \Leftrightarrow x(3x-24) = 0 \\ \Leftrightarrow x = 0 \vee 3x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{3} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
11. \(3(5x^2+2x)=-(-21x^2+16x) \\ \Leftrightarrow 15x^2+6x=21x^2-16x \\ \Leftrightarrow 15x^2+6x-21x^2+16x= 0 \\ \Leftrightarrow -6x^2-22x=0 \\ \Leftrightarrow x(-6x-22) = 0 \\ \Leftrightarrow x = 0 \vee -6x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-6} = \frac{-11}{3} \\ V = \Big\{ 0 ; \frac{-11}{3} \Big\} \\ -----------------\)
12. \(2(2x^2-3x)=-(-12x^2+12x) \\ \Leftrightarrow 4x^2-6x=12x^2-12x \\ \Leftrightarrow 4x^2-6x-12x^2+12x= 0 \\ \Leftrightarrow -8x^2-6x=0 \\ \Leftrightarrow x(-8x-6) = 0 \\ \Leftrightarrow x = 0 \vee -8x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-8} = \frac{-3}{4} \\ V = \Big\{ 0 ; \frac{-3}{4} \Big\} \\ -----------------\)