Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2+50=0\)
2. \(8x^2-1352=0\)
3. \(3x^2+0=0\)
4. \(-14x^2+152=-8x^2+2\)
5. \(-7x^2+252=-2x^2+7\)
6. \(7x^2+7=0\)
7. \(-3x^2-372=-6x^2-9\)
8. \(-8x^2-200=0\)
9. \(9x^2-6=7x^2-6\)
10. \(-10x^2+187=-6x^2-9\)
11. \(2x^2-338=0\)
12. \(11x^2-12=9x^2-4\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2+50=0 \\ \Leftrightarrow -2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{-2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
2. \(8x^2-1352=0 \\ \Leftrightarrow 8x^2 = 1352 \\ \Leftrightarrow x^2 = \frac{1352}{8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(3x^2+0=0 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-14x^2+152=-8x^2+2 \\ \Leftrightarrow -14x^2+8x^2=2-152 \\ \Leftrightarrow -6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{-6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(-7x^2+252=-2x^2+7 \\ \Leftrightarrow -7x^2+2x^2=7-252 \\ \Leftrightarrow -5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{-5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(7x^2+7=0 \\ \Leftrightarrow 7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{7} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-3x^2-372=-6x^2-9 \\ \Leftrightarrow -3x^2+6x^2=-9+372 \\ \Leftrightarrow 3x^2 = 363 \\ \Leftrightarrow x^2 = \frac{363}{3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
8. \(-8x^2-200=0 \\ \Leftrightarrow -8x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{-8} < 0 \\ V = \varnothing \\ -----------------\)
9. \(9x^2-6=7x^2-6 \\ \Leftrightarrow 9x^2-7x^2=-6+6 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-10x^2+187=-6x^2-9 \\ \Leftrightarrow -10x^2+6x^2=-9-187 \\ \Leftrightarrow -4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-4}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
11. \(2x^2-338=0 \\ \Leftrightarrow 2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(11x^2-12=9x^2-4 \\ \Leftrightarrow 11x^2-9x^2=-4+12 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)