Explanation:
We are solving 10 quadratic equations using the
Zero Property (also called the Zero Product Property) and
Square Roots. Let’s go one by one.
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1. $(k - 7)(k - 6) = 0$
Use Zero Property: If a product is 0, at least one factor is 0.
So:
$k - 7 = 0 \Rightarrow k = 7$
or
$k - 6 = 0 \Rightarrow k = 6$
✔ Solutions: $k = 6, 7$
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2. $(2t + 1)(6t - 5) = 0$
Set each factor to 0:
$2t + 1 = 0 \Rightarrow 2t = -1 \Rightarrow t = -\frac{1}{2}$
$6t - 5 = 0 \Rightarrow 6t = 5 \Rightarrow t = \frac{5}{6}$
✔ Solutions: $t = -\frac{1}{2}, \frac{5}{6}$
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3. $j^2 = 225$
Take square root of both sides:
$j = \pm \sqrt{225} = \pm 15$
✔ Solutions: $j = -15, 15$
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4. $(k + 12)(k + 10) = 0$
Set each factor to 0:
$k + 12 = 0 \Rightarrow k = -12$
$k + 10 = 0 \Rightarrow k = -10$
✔ Solutions: $k = -12, -10$
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5. $(9w - 4)(8w + 3) = 0$
$9w - 4 = 0 \Rightarrow 9w = 4 \Rightarrow w = \frac{4}{9}$
$8w + 3 = 0 \Rightarrow 8w = -3 \Rightarrow w = -\frac{3}{8}$
✔ Solutions: $w = \frac{4}{9}, -\frac{3}{8}$
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6. $u^2 = 81$
Take square root:
$u = \pm \sqrt{81} = \pm 9$
✔ Solutions: $u = -9, 9$
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7. $(f - 15)(f + 10) = 0$
$f - 15 = 0 \Rightarrow f = 15$
$f + 10 = 0 \Rightarrow f = -10$
✔ Solutions: $f = -10, 15$
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8. $(4r - 2)(10r - 8) = 0$
$4r - 2 = 0 \Rightarrow 4r = 2 \Rightarrow r = \frac{2}{4} = \frac{1}{2}$
$10r - 8 = 0 \Rightarrow 10r = 8 \Rightarrow r = \frac{8}{10} = \frac{4}{5}$
✔ Solutions: $r = \frac{1}{2}, \frac{4}{5}$
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9. $p^2 = 36$
$\sqrt{36} = \pm 6$
✔ Solutions: $p = -6, 6$
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10. $(g + 8)(g - 7) = 0$
$g + 8 = 0 \Rightarrow g = -8$
$g - 7 = 0 \Rightarrow g = 7$
✔ Solutions: $g = -8, 7$
Now let’s list all answers clearly.
Final Answer:
1. $k = 6, 7$
2. $t = -\frac{1}{2}, \frac{5}{6}$
3. $j = -15, 15$
4. $k = -12, -10$
5. $w = \frac{4}{9}, -\frac{3}{8}$
6. $u = -9, 9$
7. $f = -10, 15$
8. $r = \frac{1}{2}, \frac{4}{5}$
9. $p = -6, 6$
10. $g = -8, 7$
Parent Tip: Review the logic above to help your child master the concept of square root property worksheet.
