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bonufazy [111]
2 years ago
10

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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Please read the answers below.

Step-by-step explanation:

Let's calculate the four means between 100 and 135, this way:

1. Arithmetic mean:

(100 + 135)/2 = 117.5

2. Weighted mean:

We will assign equal weight to both numbers : 5

(100 * 5 + 135 * 5)/10 = (500 + 675)/10 = 1,175/10 = 117.5

3. Geometric mean:

√100 * 135 = √13,500 = 116.2 (Rounding to the next tenth)

4. Harmonic mean:

2/(1/100 + 1/135) = 2/(0.01 + 0.0074) = 114.9 (Rounding to the next tenth)

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Write an equation of the line that passes through the given points.<br> (-1,5) and (2, - 7)
Vanyuwa [196]

Answer:

The equation of the straight line is 4x +y = 1

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given points are (-1,5) and ( 2,-7)

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slope of the line m = -4

<u><em>Step(ii):-</em></u>

The equation of the straight line passing through the point (-1,5) and having slope 'm' = -4

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y - 5 = -4 ( x-(-1))

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<u><em>Final answer:-</em></u>

The equation of the straight line is 4x +y = 1

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Answer:

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