If the HCF of polynomials f x x 1 x2 3x a and g x x 2 x2 2x b is x2 x 2 then what are the values of ...........

Quantitative Aptitude (CDS) Number System

Download Solution PDF

If the HCF of polynomials

f(x) = (x - 1) (x² + 3x + a) and

g(x) (x + 2) (x² + 2x + b) is (x² + x - 2), then what are the values of a and b respectively ?

2, 2

2, - 3

-1, - 3

- 2, -1

छोटे Courses बड़े Results

Master Number System

Prepare through Micro-courses

Try Now

Explanation:

Since HCF of two polynomials is (??2+??−2), therefore splitting this polynomial by middle term, we get x(x+2)-(x+2) = (x-1)(x+2)
Being the HCF of the given polynomial, we conclude that (x-1) and (x+2) is a factor of f(x) and g(x)
By HCF we give the value of a and b

Since x is a factor of (x²+3x+a), therefore x = - 2 will satisfied the polynomial. Thus
x²+ 3x+a =0
=> (−2)²+ 3(−2)+ ??=0
=> ??=2
Also, since (x - 1) is a factor of (x²+2x+b), therefore x = 1 will satisfied this polynomial. Thus,
x²+ 2x+b =0 , b = -3
Hence a = 2 and b = - 3