11. On dividing 3x3 + x2 + 2x + 5 by a polynomial g(x), the quotient and
remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
12. Verify division algorithm for the polynomials f(x) = 8 + 20x +32 - 632
and g(x) = 2 + 5x – 3x?.
13. It is given that-1 is one of the zeros of the polynomial x + 27-11x-12.
Find all the zeros of the given polynomial.
14. If 1 and 2 are two zeros of the polynomial (X° - 48 - 7x + 10), find its
third zero.
15. If 3 and -3 are two zeros of the polynomial (x+ + x - 112 - 9x +18), find
all the zeros of the given polynomial.
16. If 2 and 2 are two zeros of the polynomial 2x4 – 5r-11r + 20x + 12,
find all the zeros of the given polynomial.
(CBSE 2019]
Answers
Given : On dividing 3x³+ x² + 2x + 5 by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively.
To Find : g(x).
Solution:
P(x) = g(x)q(x) + r(x)
=>3x³+ x² + 2x + 5 = g(x)(3x - 5) + 9x + 10
=> g(x)(3x - 5) = 3x³+ x² + 2x + 5 - 9x - 10
=> g(x)(3x - 5) = 3x³+ x² -7x - 5
=> g(x) = (3x³+ x² -7x - 5)/(3x - 5)
x² + 2x + 1
3x - 5 _| 3x³+ x² -7x - 5 |_
3x³ -5x²
___________
6x² -7x - 5
6x² - 10x
__________
3x - 5
3x - 5
________
0
g(x) = x² + 2x + 1
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