Question

Find the zeros of the following expressions by factoring.

a. y

2 – 8 – 20 = 0

b. r

2 + 3r – 54 = 0

c. h

2 – h = 0

d. x

2 – 49 = 0

e. n

2 + 6n + 8 = 0

f. y

2 + 16y + 64 = 0

g. n

2 – 3n = 0​

Answer 1

Answer:

Step-by-step explanation:

1). a² - b² = (a - b)(a + b)

2). (a ± b)² = a² ± 2ab + b²

3). ax² + bx + c = a(x - $x_{1}$ )(x - $x_{2}$ )

$x_{1}$ + $x_{2}$ = - $\frac{b}{a}$

$x_{1}$$x_{2}$ = $\frac{c}{a}$

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a). y² - 8y - 20 = 0

(y - 10)(y + 2) = 0 ⇒ $y_{1}$ = 10 and $y_{2}$ = - 2

b). r² + 3r - 54 = 0 ⇔ (r + 9)(r - 6) = 0 ⇒ $r_{1}$ = - 9 and $r_{2}$ = 6

c). h² - h = 0 ⇔ h(h - 1) = 0 ⇒ $h_{1}$ = 0 and $h_{2}$ = 1

d). x² - 49 = 0

x² - 7² = 0 ⇔ (x - 7)(x + 7) = 0 ⇒ $x_{12}$ = ± 7

f). y² + 16y + 64 = 0

y² + 2*8*y + 8² = 0 ⇔ (y + 8)² = 0 ⇒ $y_{12}$ = 8 (given equation has two equal roots)

You have all the ideas to be able to solve (e) and (g), it's good for your practice.... and ... NOW IS YOUR TURN :)