Question

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

Answer 1

A = 1, B = 7, C = 4

Explanation:

`2x^2 +5x-C= 2(x - 2)(Ax+1)+Bx\\</p><p>2x^2 +5x-C= (2x - 4)(Ax+1)+Bx\\</p><p>2x^2 +5x-C= 2Ax^2+2x - 4Ax-4+Bx\\</p><p>2x^2 +5x-C= 2Ax^2 + (2-4A+B)x-4\\`

Equating like terms on both sides:

`2x^2 = 2Ax^2\\</p><p>(2x^2)/(2x^2) = A\\</p><p>\huge \purple {\boxed {\implies A = 1}} \\\\</p><p>5x = (2-4A+B)x\\</p><p>(5x)/(x) =2-4A + B\\</p><p>2-4A + B = 5....(1)\\</p><p>[Plug \: A = 1\: in\: equation \: (1)] \\</p><p>2-4* 1 + B = 5\\</p><p>2-4 +B = 5\\</p><p>-2 + B = 5\\</p><p>B=5+2\\</p><p>\huge \purple {\boxed {\implies B = 7}} \\\\</p><p>-C = - 4\\</p><p>\huge \purple {\boxed {\implies C = 4}}`