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2 years ago

X-3 and 2x-1 are factors of 2x^3-px^2-2qx+q. Find the values of p and q.

Mathematics

1 answer:

Nonamiya [84]2 years ago

8 0

Answer:

p =1

q = 9

Step-by-step explanation:

f(x) = 2x³ - px² + 2qx + q

(x - 3) is a factor of f(x)

⇒f(3) = 0

2(3)³ - p*3² - 2q*3 +q = 0

2*27 - 9p - 6q + q = 0

54 - 9p - 5q = 0

-9p - 5q = -54 -------------------(I)

(2x - 1) is a factor of f(x)

2x - 1 = 0

2x = 1

$\st x = \dfrac{1}{2}$

f(1/2) = 0

$2*(\dfrac{1}{2})^{3}-p*(\dfrac{1}{2})^{2}-2q*\dfrac{1}{2}+q=0\\\\2*\dfrac{1}{8}-p*\dfrac{1}{4}-q+q = 0\\\\\dfrac{1}{4}-\dfrac{1}{4}p =0\\\\[Multiply the entire equation by 4]\\\\4*\dfrac{1}{4}-4*\dfrac{1}{4}p=0\\\\$

1 - p = 0

-p = -1

p = 1

Substitute p =1 in equation (I)

-9*1 - 5q = -54

-9 - 5q = -54

-5q = -54 + 9

-5q = -45

q = -45/(-5)

q = 9

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Answer:

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To test for convergence or divergence using ratio test, we will use the condition above.

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aₙ₊₁/aₙ =

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3 years ago

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serg [7]

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3 years ago

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GaryK [48]

Answer:

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Step-by-step explanation:

Factor the following:

7 x^2 + 6 x - 1

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3 years ago

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Answer:

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Step-by-step explanation:

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