Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(8x^2+17x=0\)
2. \(5x^2+19x=10x^2+2x\)
3. \(-7x^2+18x=-2x^2+3x\)
4. \(3(-6x^2+2x)=-(10x^2+10x)\)
5. \(-8x^2+24x=0\)
6. \(-2x^2-10x=0\)
7. \(2(7x^2-3x)=-(-12x^2+18x)\)
8. \(-3x^2-2x=-10x^2+8x\)
9. \(-7x^2-25x=0\)
10. \(-8x^2-22x=0\)
11. \(3x^2-10x=0\)
12. \(-4x^2+18x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(8x^2+17x=0 \\ \Leftrightarrow x(8x+17) = 0 \\ \Leftrightarrow x = 0 \vee 8x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{8} \\ V = \Big\{ 0 ; \frac{-17}{8} \Big\} \\ -----------------\)
2. \(5x^2+19x=10x^2+2x \\ \Leftrightarrow -5x^2+17x=0 \\ \Leftrightarrow x(-5x+17) = 0 \\ \Leftrightarrow x = 0 \vee -5x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-5} = \frac{17}{5} \\ V = \Big\{ \frac{17}{5}; 0 \Big\} \\ -----------------\)
3. \(-7x^2+18x=-2x^2+3x \\ \Leftrightarrow -5x^2+15x=0 \\ \Leftrightarrow x(-5x+15) = 0 \\ \Leftrightarrow x = 0 \vee -5x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-5} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
4. \(3(-6x^2+2x)=-(10x^2+10x) \\ \Leftrightarrow -18x^2+6x=-10x^2-10x \\ \Leftrightarrow -18x^2+6x+10x^2+10x= 0 \\ \Leftrightarrow -8x^2-16x=0 \\ \Leftrightarrow x(-8x-16) = 0 \\ \Leftrightarrow x = 0 \vee -8x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-8} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
5. \(-8x^2+24x=0 \\ \Leftrightarrow x(-8x+24) = 0 \\ \Leftrightarrow x = 0 \vee -8x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-8} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
6. \(-2x^2-10x=0 \\ \Leftrightarrow x(-2x-10) = 0 \\ \Leftrightarrow x = 0 \vee -2x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-2} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
7. \(2(7x^2-3x)=-(-12x^2+18x) \\ \Leftrightarrow 14x^2-6x=12x^2-18x \\ \Leftrightarrow 14x^2-6x-12x^2+18x= 0 \\ \Leftrightarrow 2x^2-12x=0 \\ \Leftrightarrow x(2x-12) = 0 \\ \Leftrightarrow x = 0 \vee 2x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{2} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
8. \(-3x^2-2x=-10x^2+8x \\ \Leftrightarrow 7x^2-10x=0 \\ \Leftrightarrow x(7x-10) = 0 \\ \Leftrightarrow x = 0 \vee 7x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{7} \\ V = \Big\{ \frac{10}{7}; 0 \Big\} \\ -----------------\)
9. \(-7x^2-25x=0 \\ \Leftrightarrow x(-7x-25) = 0 \\ \Leftrightarrow x = 0 \vee -7x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-7} = \frac{-25}{7} \\ V = \Big\{ 0 ; \frac{-25}{7} \Big\} \\ -----------------\)
10. \(-8x^2-22x=0 \\ \Leftrightarrow x(-8x-22) = 0 \\ \Leftrightarrow x = 0 \vee -8x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-8} = \frac{-11}{4} \\ V = \Big\{ 0 ; \frac{-11}{4} \Big\} \\ -----------------\)
11. \(3x^2-10x=0 \\ \Leftrightarrow x(3x-10) = 0 \\ \Leftrightarrow x = 0 \vee 3x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)
12. \(-4x^2+18x=0 \\ \Leftrightarrow x(-4x+18) = 0 \\ \Leftrightarrow x = 0 \vee -4x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-4} = \frac{9}{2} \\ V = \Big\{ \frac{9}{2}; 0 \Big\} \\ -----------------\)