RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 2. Polynomials

Subject: Maths - Class 10th

Q. No. 14 of CCE - Formative Assessment

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14

If the polynomial f(x) = ax3 + bx – c is divisible by the polynomial g(x) = x2 + bx + c, then ab =

Given;


f(x) = ax3 + bx – c is divisible by g(x) = x2 + bx + c


Now by division Method,



As f(x) is divisible by g(x), then remainder must be 0,


i.e.


(ab2 – ac + b)x + c(ab – 1) = 0


(ab2 – ac + b)x = 0 and c(ab – 1) = 0


ab2 – ab + b = 0 ( x 0) and ab 1 = 0 ( c 0)


ab – 1 = 0


ab = 1

14

Chapter Exercises

More Exercise Questions

8

The sum and product of the zeros of a quadratic polynomial are and — 3 respectively. What is the quadratic polynomial?