Mathematics: Let A,B.and C be the constants. Find the values of A,B and C.

B. The range of F(x) is y and gt;0....

Let A,B.and C be the constants. Find the values

Ответ:

DylanJF1339

03.02.2022

Mathematics

A = 1, B = 7, C = 4

Step-by-step explanation:

$2x^2 +5x-C= 2(x - 2)(Ax+1)+Bx\\2x^2 +5x-C= (2x - 4)(Ax+1)+Bx\\2x^2 +5x-C= 2Ax^2+2x - 4Ax-4+Bx\\2x^2 +5x-C= 2Ax^2 + (2-4A+B)x-4\\$

Equating like terms on both sides:

$2x^2 = 2Ax^2\\\frac{2x^2}{2x^2} = A\\\huge \purple {\boxed {\implies A = 1}} \\\\5x = (2-4A+B)x\\\frac{5x}{x} =2-4A + B\\2-4A + B = 5....(1)\\[Plug \: A = 1\: in\: equation \: (1)] \\2-4\times 1 + B = 5\\2-4 +B = 5\\-2 + B = 5\\B=5+2\\\huge \purple {\boxed {\implies B = 7}} \\\\-C = - 4\\\huge \purple {\boxed {\implies C = 4}}$

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Let A,B.and C be the constants. Find the values of A,B and C.

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