Question

2. Let f(x) = 5x² - 2x - 7.
(a) find f(0)
(b) find f(-3)
(c) find x if f(x) = 0

Answer 1

A) f(0) = -7

B) f(-3) = 44

C) x = -1, (7/5)

Explanation:

2. Let f(x) = 5x² - 2x - 7.

(a) find f(0)

f(x) = 5x² - 2x - 7

f(0) = 5(0)² - 2(0) - 7

f(0) = -7

(b) find f(-3)

f(x) = 5x² - 2x - 7

f(-3) = 5(-3)² - 2(-3) - 7

f(-3) = 5(9) - 2(-3) - 7

f(-3) = 45 + 6 - 7

f(-3) = 45 + 6 - 7

f(-3) = 44

(c) find x if f(x) = 0

f(x) = 5x² - 2x - 7

f(x) = 5x² - 2x - 7 = 0

(5x² + 5x)(-7x - 7)

5x(x + 1) -7(x + 1)

(5x - 7)(x + 1)

5x - 7 = 0, x + 1 = 0

+7 +7 -1 -1

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5x = 7 x = -1

÷5 ÷5

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x = (7/5)

5(-1)² - 2(-1) - 7 = 0

5(7/5)² - 2(7/5) - 7 = 0

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I hope this helps!

Answer 2

(A) f(0) = 5*0 - 2*0 - 7 = -7
(B) Same calcul with -3 f(-3) = 25
(C) delta = b^2 - 4ac
= -2^2 - 4*5*(-7)
= 4 + 140
= 144 so delta>0 2 solutions
X1 = -10/10 = -1
X2 = 14/10 = 7/5