4.5E: Exercises
- Page ID
- 108359
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Practice Makes Perfect
- \(x^2 - x - 6 = 0\)
- \(3x^2 + 7x + 4 = 0\)
- \(m^2 +5x + 4 = 0\)
- \(-2a^2 + 6a - 4 = 0\)
- \(p^2 + 11p + 30 = 0\)
- \(y^2 -18y + 45 = 0\)
Some problems need to be rearranged a bit to fit the format \(ax^2 + bx + c = 0\) before factoring to solve:
- \(a^2 + 25 + 50 = -50\)
- \(p^2 + 3p + 67 = -16p + 19\)
- \(-21b = 5b^2 + 4\)
- \(60y^2 + 290y = 50\)
- Answer
-
- \(x = 3, x = -2\)
- \(x = -\frac{1}{3}, x = -1\)
- \(m = -1, m = -4\)
- \(a = 1, a = 2\)
- \(p = -5, p = -6\)
- \( y = 3, y = 15\)
- \(a = -5\)
- \(p = -3, p = -16\)
- \(b = -\frac{1}{5}, b = -4\)
- \(y = \frac{1}{6}, y = -5\)
In the following exercises, solve each equation.
- \(a^{2}=49\)
- \(r^{2}-24=0\)
- \(u^{2}-300=0\)
- \(4 m^{2}=36\)
- \(\frac{4}{3} x^{2}=48\)
- \(x^{2}+25=0\)
- \(x^{2}+63=0\)
- \(\frac{4}{3} x^{2}+2=110\)
- \(\frac{2}{5} a^{2}+3=11\)
- \(7 p^{2}+10=26\)
- \(5 y^{2}-7=25\)
- Answer
-
- \(a=\pm 7\)
- \(r=\pm 2 \sqrt{6}\)
- \(u=\pm 10 \sqrt{3}\)
- \(m=\pm 3\)
- \(x=\pm 6\)
- \(x=\pm 5 i\)
- \(x=\pm 3 \sqrt{7} i\)
- \(x=\pm 9\)
- \(a=\pm 2 \sqrt{5}\)
- \(p=\pm \frac{4}{\sqrt{7}}\)
- \(y=\pm \frac{4 \sqrt{2}}{\sqrt{5}}\)
In the following exercises, solve by using the Quadratic Formula.
- \(4 m^{2}+m-3=0\)
- \(2 p^{2}-7 p+3=0\)
- \(p^{2}+7 p+12=0\)
- \(r^{2}-8 r=33\)
- \(3 u^{2}+7 u-2=0\)
- \(2 a^{2}-6 a+3=0\)
- \(x^{2}+8 x-4=0\)
- \(3 y^{2}+5 y-2=0\)
- \(2 x^{2}+3 x+3=0\)
- \(8 x^{2}-6 x+2=0\)
- \((v+1)(v-5)-4=0\)
- \(\dfrac{1}{4} m^{2}+\dfrac{1}{12} m=\dfrac{1}{3}\)
- \(16 c^{2}+24 c+9=0\)
- \(25 q^{2}+30 q+9=0\)
- Answer
-
- \(m=-1, m=\dfrac{3}{4}\)
- \(p=\dfrac{1}{2}, p=3\)
- \(p=-4, p=-3\)
- \(r=-3, r=11\)
- \(u=\dfrac{-7 \pm \sqrt{73}}{6}\)
- \(a=\dfrac{3 \pm \sqrt{3}}{2}\)
- \(x=-4 \pm 2 \sqrt{5}\)
- \(y=\dfrac{1}{3}, y=-2\)
- \(x=-\dfrac{3}{4} \pm \dfrac{\sqrt{15}}{4} i\)
- \(x=\dfrac{3}{8} \pm \dfrac{\sqrt{7}}{8} i\)
- \(v=2 \pm \sqrt{13}\)
- \(m=1, m=\dfrac{-4}{3}\)
- \(c=-\dfrac{3}{4}\)
- \(q=-\dfrac{3}{5}\)
36. In the following exercises, determine the number of real solutions for each quadratic equation.
- \(4 x^{2}-5 x+16=0\)
- \(36 y^{2}+36 y+9=0\)
- \(6 m^{2}+3 m-5=0\)
- Answer
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36. a. no real solutions b. \(1\) c. \(2\)
37. In the following exercises, determine the number of real solutions for each quadratic equation.
- \(r^{2}+12 r+36=0\)
- \(8 t^{2}-11 t+5=0\)
- \(3 v^{2}-5 v-1=0\)
- Answer
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37. a. \(1\) b. no real solutions c. \(2\)