Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2+20x=0\)
2. \(9x^2+16x=8x^2+5x\)
3. \(-x^2+23x=0\)
4. \(4(-8x^2+9x)=-(29x^2-61x)\)
5. \(2x^2-18x=-4x^2+2x\)
6. \(-10x^2-19x=-7x^2-9x\)
7. \(-7x^2-11x=0\)
8. \(-3(-10x^2+4x)=-(-25x^2+24x)\)
9. \(-6x^2-22x=2x^2-2x\)
10. \(2(-7x^2-2x)=-(13x^2-x)\)
11. \(3(4x^2+7x)=-(-20x^2-41x)\)
12. \(-3x^2-29x=-7x^2-8x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2+20x=0 \\ \Leftrightarrow x(5x+20) = 0 \\ \Leftrightarrow x = 0 \vee 5x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{5} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
2. \(9x^2+16x=8x^2+5x \\ \Leftrightarrow x^2+11x=0 \\ \Leftrightarrow x(x+11) = 0 \\ \Leftrightarrow x = 0 \vee x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{1} = -11 \\ V = \Big\{ 0 ; -11 \Big\} \\ -----------------\)
3. \(-x^2+23x=0 \\ \Leftrightarrow x(-x+23) = 0 \\ \Leftrightarrow x = 0 \vee -x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-1} = 23 \\ V = \Big\{ 23; 0 \Big\} \\ -----------------\)
4. \(4(-8x^2+9x)=-(29x^2-61x) \\ \Leftrightarrow -32x^2+36x=-29x^2+61x \\ \Leftrightarrow -32x^2+36x+29x^2-61x= 0 \\ \Leftrightarrow -3x^2+25x=0 \\ \Leftrightarrow x(-3x+25) = 0 \\ \Leftrightarrow x = 0 \vee -3x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-3} = \frac{25}{3} \\ V = \Big\{ \frac{25}{3}; 0 \Big\} \\ -----------------\)
5. \(2x^2-18x=-4x^2+2x \\ \Leftrightarrow 6x^2-20x=0 \\ \Leftrightarrow x(6x-20) = 0 \\ \Leftrightarrow x = 0 \vee 6x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{6} = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)
6. \(-10x^2-19x=-7x^2-9x \\ \Leftrightarrow -3x^2-10x=0 \\ \Leftrightarrow x(-3x-10) = 0 \\ \Leftrightarrow x = 0 \vee -3x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-3} = \frac{-10}{3} \\ V = \Big\{ 0 ; \frac{-10}{3} \Big\} \\ -----------------\)
7. \(-7x^2-11x=0 \\ \Leftrightarrow x(-7x-11) = 0 \\ \Leftrightarrow x = 0 \vee -7x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-7} = \frac{-11}{7} \\ V = \Big\{ 0 ; \frac{-11}{7} \Big\} \\ -----------------\)
8. \(-3(-10x^2+4x)=-(-25x^2+24x) \\ \Leftrightarrow 30x^2-12x=25x^2-24x \\ \Leftrightarrow 30x^2-12x-25x^2+24x= 0 \\ \Leftrightarrow 5x^2-12x=0 \\ \Leftrightarrow x(5x-12) = 0 \\ \Leftrightarrow x = 0 \vee 5x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{5} \\ V = \Big\{ \frac{12}{5}; 0 \Big\} \\ -----------------\)
9. \(-6x^2-22x=2x^2-2x \\ \Leftrightarrow -8x^2-20x=0 \\ \Leftrightarrow x(-8x-20) = 0 \\ \Leftrightarrow x = 0 \vee -8x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-8} = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
10. \(2(-7x^2-2x)=-(13x^2-x) \\ \Leftrightarrow -14x^2-4x=-13x^2+x \\ \Leftrightarrow -14x^2-4x+13x^2-x= 0 \\ \Leftrightarrow -x^2+5x=0 \\ \Leftrightarrow x(-x+5) = 0 \\ \Leftrightarrow x = 0 \vee -x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-1} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
11. \(3(4x^2+7x)=-(-20x^2-41x) \\ \Leftrightarrow 12x^2+21x=20x^2+41x \\ \Leftrightarrow 12x^2+21x-20x^2-41x= 0 \\ \Leftrightarrow -8x^2+20x=0 \\ \Leftrightarrow x(-8x+20) = 0 \\ \Leftrightarrow x = 0 \vee -8x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-8} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
12. \(-3x^2-29x=-7x^2-8x \\ \Leftrightarrow 4x^2-21x=0 \\ \Leftrightarrow x(4x-21) = 0 \\ \Leftrightarrow x = 0 \vee 4x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{4} \\ V = \Big\{ \frac{21}{4}; 0 \Big\} \\ -----------------\)