Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2+19x=0\)
2. \(-2(-7x^2-3x)=-(-9x^2-20x)\)
3. \(7x^2+21x=0\)
4. \(-4(10x^2-5x)=-(45x^2-5x)\)
5. \(-2x^2+16x=0\)
6. \(-3x^2+20x=0\)
7. \(x^2-25x=0\)
8. \(13x^2+9x=6x^2+4x\)
9. \(12x^2+21x=4x^2+3x\)
10. \(-4x^2+1x=0\)
11. \(-11x^2-30x=-5x^2-10x\)
12. \(-7x^2-10x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2+19x=0 \\ \Leftrightarrow x(2x+19) = 0 \\ \Leftrightarrow x = 0 \vee 2x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{2} \\ V = \Big\{ 0 ; \frac{-19}{2} \Big\} \\ -----------------\)
2. \(-2(-7x^2-3x)=-(-9x^2-20x) \\ \Leftrightarrow 14x^2+6x=9x^2+20x \\ \Leftrightarrow 14x^2+6x-9x^2-20x= 0 \\ \Leftrightarrow 5x^2+14x=0 \\ \Leftrightarrow x(5x+14) = 0 \\ \Leftrightarrow x = 0 \vee 5x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{5} \\ V = \Big\{ 0 ; \frac{-14}{5} \Big\} \\ -----------------\)
3. \(7x^2+21x=0 \\ \Leftrightarrow x(7x+21) = 0 \\ \Leftrightarrow x = 0 \vee 7x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{7} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
4. \(-4(10x^2-5x)=-(45x^2-5x) \\ \Leftrightarrow -40x^2+20x=-45x^2+5x \\ \Leftrightarrow -40x^2+20x+45x^2-5x= 0 \\ \Leftrightarrow 5x^2-15x=0 \\ \Leftrightarrow x(5x-15) = 0 \\ \Leftrightarrow x = 0 \vee 5x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{5} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
5. \(-2x^2+16x=0 \\ \Leftrightarrow x(-2x+16) = 0 \\ \Leftrightarrow x = 0 \vee -2x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-2} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
6. \(-3x^2+20x=0 \\ \Leftrightarrow x(-3x+20) = 0 \\ \Leftrightarrow x = 0 \vee -3x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-3} = \frac{20}{3} \\ V = \Big\{ \frac{20}{3}; 0 \Big\} \\ -----------------\)
7. \(x^2-25x=0 \\ \Leftrightarrow x(x-25) = 0 \\ \Leftrightarrow x = 0 \vee x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{1} = 25 \\ V = \Big\{ 25; 0 \Big\} \\ -----------------\)
8. \(13x^2+9x=6x^2+4x \\ \Leftrightarrow 7x^2+5x=0 \\ \Leftrightarrow x(7x+5) = 0 \\ \Leftrightarrow x = 0 \vee 7x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{7} \\ V = \Big\{ 0 ; \frac{-5}{7} \Big\} \\ -----------------\)
9. \(12x^2+21x=4x^2+3x \\ \Leftrightarrow 8x^2+18x=0 \\ \Leftrightarrow x(8x+18) = 0 \\ \Leftrightarrow x = 0 \vee 8x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{8} = \frac{-9}{4} \\ V = \Big\{ 0 ; \frac{-9}{4} \Big\} \\ -----------------\)
10. \(-4x^2+1x=0 \\ \Leftrightarrow x(-4x+1) = 0 \\ \Leftrightarrow x = 0 \vee -4x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-4} = \frac{1}{4} \\ V = \Big\{ \frac{1}{4}; 0 \Big\} \\ -----------------\)
11. \(-11x^2-30x=-5x^2-10x \\ \Leftrightarrow -6x^2-20x=0 \\ \Leftrightarrow x(-6x-20) = 0 \\ \Leftrightarrow x = 0 \vee -6x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-6} = \frac{-10}{3} \\ V = \Big\{ 0 ; \frac{-10}{3} \Big\} \\ -----------------\)
12. \(-7x^2-10x=0 \\ \Leftrightarrow x(-7x-10) = 0 \\ \Leftrightarrow x = 0 \vee -7x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-7} = \frac{-10}{7} \\ V = \Big\{ 0 ; \frac{-10}{7} \Big\} \\ -----------------\)