Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(-5x^2+10x)=-(11x^2-12x)\)
2. \(-2x^2+11x=-10x^2-9x\)
3. \(-x^2-18x=0\)
4. \(5(7x^2-3x)=-(-38x^2+14x)\)
5. \(-5(-10x^2-4x)=-(-53x^2-4x)\)
6. \(8x^2+12x=0\)
7. \(3x^2+4x=0\)
8. \(-8x^2-3x=0\)
9. \(2(-7x^2+5x)=-(10x^2-8x)\)
10. \(4x^2+25x=7x^2+3x\)
11. \(3x^2-6x=5x^2+4x\)
12. \(-6x^2-15x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(-5x^2+10x)=-(11x^2-12x) \\ \Leftrightarrow -15x^2+30x=-11x^2+12x \\ \Leftrightarrow -15x^2+30x+11x^2-12x= 0 \\ \Leftrightarrow -4x^2-18x=0 \\ \Leftrightarrow x(-4x-18) = 0 \\ \Leftrightarrow x = 0 \vee -4x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-4} = \frac{-9}{2} \\ V = \Big\{ 0 ; \frac{-9}{2} \Big\} \\ -----------------\)
2. \(-2x^2+11x=-10x^2-9x \\ \Leftrightarrow 8x^2+20x=0 \\ \Leftrightarrow x(8x+20) = 0 \\ \Leftrightarrow x = 0 \vee 8x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{8} = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
3. \(-x^2-18x=0 \\ \Leftrightarrow x(-x-18) = 0 \\ \Leftrightarrow x = 0 \vee -x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-1} = -18 \\ V = \Big\{ 0 ; -18 \Big\} \\ -----------------\)
4. \(5(7x^2-3x)=-(-38x^2+14x) \\ \Leftrightarrow 35x^2-15x=38x^2-14x \\ \Leftrightarrow 35x^2-15x-38x^2+14x= 0 \\ \Leftrightarrow -3x^2+1x=0 \\ \Leftrightarrow x(-3x+1) = 0 \\ \Leftrightarrow x = 0 \vee -3x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-3} = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
5. \(-5(-10x^2-4x)=-(-53x^2-4x) \\ \Leftrightarrow 50x^2+20x=53x^2+4x \\ \Leftrightarrow 50x^2+20x-53x^2-4x= 0 \\ \Leftrightarrow -3x^2-16x=0 \\ \Leftrightarrow x(-3x-16) = 0 \\ \Leftrightarrow x = 0 \vee -3x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-3} = \frac{-16}{3} \\ V = \Big\{ 0 ; \frac{-16}{3} \Big\} \\ -----------------\)
6. \(8x^2+12x=0 \\ \Leftrightarrow x(8x+12) = 0 \\ \Leftrightarrow x = 0 \vee 8x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{8} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
7. \(3x^2+4x=0 \\ \Leftrightarrow x(3x+4) = 0 \\ \Leftrightarrow x = 0 \vee 3x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{3} \\ V = \Big\{ 0 ; \frac{-4}{3} \Big\} \\ -----------------\)
8. \(-8x^2-3x=0 \\ \Leftrightarrow x(-8x-3) = 0 \\ \Leftrightarrow x = 0 \vee -8x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-8} = \frac{-3}{8} \\ V = \Big\{ 0 ; \frac{-3}{8} \Big\} \\ -----------------\)
9. \(2(-7x^2+5x)=-(10x^2-8x) \\ \Leftrightarrow -14x^2+10x=-10x^2+8x \\ \Leftrightarrow -14x^2+10x+10x^2-8x= 0 \\ \Leftrightarrow -4x^2-2x=0 \\ \Leftrightarrow x(-4x-2) = 0 \\ \Leftrightarrow x = 0 \vee -4x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-4} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
10. \(4x^2+25x=7x^2+3x \\ \Leftrightarrow -3x^2+22x=0 \\ \Leftrightarrow x(-3x+22) = 0 \\ \Leftrightarrow x = 0 \vee -3x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-3} = \frac{22}{3} \\ V = \Big\{ \frac{22}{3}; 0 \Big\} \\ -----------------\)
11. \(3x^2-6x=5x^2+4x \\ \Leftrightarrow -2x^2-10x=0 \\ \Leftrightarrow x(-2x-10) = 0 \\ \Leftrightarrow x = 0 \vee -2x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-2} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
12. \(-6x^2-15x=0 \\ \Leftrightarrow x(-6x-15) = 0 \\ \Leftrightarrow x = 0 \vee -6x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-6} = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)