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elena-s [515]
2 years ago
11

Given that the expression x³_ ax² + bx+c leaves the same remainder when divided by x + 1 or x-2, find 'a' in terms of 'b'.​

Mathematics
1 answer:
goblinko [34]2 years ago
5 0

Answer:

Hi,

a=b+3

Step-by-step explanation:

\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&c-a-b-1\\\end{array}

\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=2&&2&4-2a&2b+8-4a\\---&---&---&---&---\\&1&2-a&b+4-2a&c+2b+8-4a\\\end{array}

Thus:

c+2b+8-4a=c-a-b-1

3b-3a=-9

<u>a=b+3</u>

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6 0
3 years ago
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In Rhombus ABCD if BD is 24 ft and AD is 15 ft, then what is the length of AC?
Evgen [1.6K]

Answer:

AC = 24ft

Step by Step Explanation.

Given.

Rhombus.

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Required

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The opposite sides of a parallelogram are always of equal length

From the attached diagram (not drawn to scale), side AC opposites side BD

Given that BD = 24ft, then

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3 years ago
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s344n2d4d5 [400]

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

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Comparing with the slope intercept form,

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To determine c,

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Step-by-step explanation:

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3 years ago
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