Question

when ax^2 + bx - 1 is added to ax^3 + 2bx^2 - 2x -1, the result is 3x^3 + 11x^2 + 2x -c. find a, b, and c

Answer 1

The values of a,b and c are 3,4 and 2 respectively

Further explanation:

In questions like these, equating the coefficients method is used:

Given

$A = ax^2 + bx - 1\\B = ax^3 + 2bx^2 - 2x -1\\S=3x^3 + 11x^2 + 2x -c$

So,

$A+B =s\\(ax^2 + bx - 1)+(ax^3 + 2bx^2 - 2x -1)=3x^3 + 11x^2 + 2x -c\\ax^2 + bx - 1+ax^3 + 2bx^2 - 2x -1=3x^3 + 11x^2 + 2x -c\\Combining alike terms\\ax^3+ax^2+2bx^2+bx+- 2x-1-1=3x^3 + 11x^2 + 2x -c\\ax^3+(a+2b)x^2+(b- 2)x-2=3x^3 + 11x^2 + 2x -c\\Comparing\ the\ co-effcients\ of\ x^3\, we\ get\\a = 3\\Comparing\ the\ co-effcients\ of\ x^2\, we\ get\\a+2b=11\\3+2b=11\\2b=11-3\\2b=8\\b=4\\And\ comaring\ the\ co-efficients\ we\ get\\-2=-c\\c=2$

Hence,

The values of a,b and c are 3,4 and 2 respectively

Keywords: Algebraic expressions, polynomials

Learn more about polynomials at:

• brainly.com/question/9045597
• brainly.com/question/9381080

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