Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(-4x^2+5x)=-(10x^2-26x)\)
2. \(-5(-10x^2-7x)=-(-42x^2-14x)\)
3. \(-4x^2+23x=0\)
4. \(-5(-4x^2-8x)=-(-18x^2-17x)\)
5. \(-5x^2-24x=0\)
6. \(-5x^2-15x=0\)
7. \(-2x^2+3x=-9x^2-2x\)
8. \(2x^2+17x=0\)
9. \(3(-10x^2+5x)=-(29x^2-9x)\)
10. \(-3x^2+15x=0\)
11. \(-5(-8x^2+2x)=-(-38x^2+10x)\)
12. \(5(6x^2-4x)=-(-28x^2+38x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(-4x^2+5x)=-(10x^2-26x) \\ \Leftrightarrow -16x^2+20x=-10x^2+26x \\ \Leftrightarrow -16x^2+20x+10x^2-26x= 0 \\ \Leftrightarrow -6x^2+6x=0 \\ \Leftrightarrow x(-6x+6) = 0 \\ \Leftrightarrow x = 0 \vee -6x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-6} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
2. \(-5(-10x^2-7x)=-(-42x^2-14x) \\ \Leftrightarrow 50x^2+35x=42x^2+14x \\ \Leftrightarrow 50x^2+35x-42x^2-14x= 0 \\ \Leftrightarrow 8x^2-21x=0 \\ \Leftrightarrow x(8x-21) = 0 \\ \Leftrightarrow x = 0 \vee 8x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{8} \\ V = \Big\{ \frac{21}{8}; 0 \Big\} \\ -----------------\)
3. \(-4x^2+23x=0 \\ \Leftrightarrow x(-4x+23) = 0 \\ \Leftrightarrow x = 0 \vee -4x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-4} = \frac{23}{4} \\ V = \Big\{ \frac{23}{4}; 0 \Big\} \\ -----------------\)
4. \(-5(-4x^2-8x)=-(-18x^2-17x) \\ \Leftrightarrow 20x^2+40x=18x^2+17x \\ \Leftrightarrow 20x^2+40x-18x^2-17x= 0 \\ \Leftrightarrow 2x^2-23x=0 \\ \Leftrightarrow x(2x-23) = 0 \\ \Leftrightarrow x = 0 \vee 2x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{2} \\ V = \Big\{ \frac{23}{2}; 0 \Big\} \\ -----------------\)
5. \(-5x^2-24x=0 \\ \Leftrightarrow x(-5x-24) = 0 \\ \Leftrightarrow x = 0 \vee -5x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-5} = \frac{-24}{5} \\ V = \Big\{ 0 ; \frac{-24}{5} \Big\} \\ -----------------\)
6. \(-5x^2-15x=0 \\ \Leftrightarrow x(-5x-15) = 0 \\ \Leftrightarrow x = 0 \vee -5x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-5} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
7. \(-2x^2+3x=-9x^2-2x \\ \Leftrightarrow 7x^2+5x=0 \\ \Leftrightarrow x(7x+5) = 0 \\ \Leftrightarrow x = 0 \vee 7x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{7} \\ V = \Big\{ 0 ; \frac{-5}{7} \Big\} \\ -----------------\)
8. \(2x^2+17x=0 \\ \Leftrightarrow x(2x+17) = 0 \\ \Leftrightarrow x = 0 \vee 2x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{2} \\ V = \Big\{ 0 ; \frac{-17}{2} \Big\} \\ -----------------\)
9. \(3(-10x^2+5x)=-(29x^2-9x) \\ \Leftrightarrow -30x^2+15x=-29x^2+9x \\ \Leftrightarrow -30x^2+15x+29x^2-9x= 0 \\ \Leftrightarrow -x^2-6x=0 \\ \Leftrightarrow x(-x-6) = 0 \\ \Leftrightarrow x = 0 \vee -x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-1} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
10. \(-3x^2+15x=0 \\ \Leftrightarrow x(-3x+15) = 0 \\ \Leftrightarrow x = 0 \vee -3x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-3} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
11. \(-5(-8x^2+2x)=-(-38x^2+10x) \\ \Leftrightarrow 40x^2-10x=38x^2-10x \\ \Leftrightarrow 40x^2-10x-38x^2+10x= 0 \\ \Leftrightarrow 2x^2+0x=0 \\ \Leftrightarrow 2x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{2} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(5(6x^2-4x)=-(-28x^2+38x) \\ \Leftrightarrow 30x^2-20x=28x^2-38x \\ \Leftrightarrow 30x^2-20x-28x^2+38x= 0 \\ \Leftrightarrow 2x^2-18x=0 \\ \Leftrightarrow x(2x-18) = 0 \\ \Leftrightarrow x = 0 \vee 2x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{2} = 9 \\ V = \Big\{ 9; 0 \Big\} \\ -----------------\)