MATH SOLVE

2 months ago

Q:
# 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

Accepted Solution

A:

The values of a,b and c are 3,4 and 2 respectivelyFurther explanation:In questions like these, equating the coefficients method is used:Given[tex]A = ax^2 + bx - 1\\B = ax^3 + 2bx^2 - 2x -1\\S=3x^3 + 11x^2 + 2x -c[/tex]So,[tex]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[/tex]Hence,The values of a,b and c are 3,4 and 2 respectivelyKeywords: Algebraic expressions, polynomialsLearn more about polynomials at:brainly.com/question/9045597brainly.com/question/9381080#LearnwithBrainly