IIT JEE , AIEEE Forum - Mathematics , Algebra

aishvar2

the H.C.F and L.C.M of the two polynomials p(x) and q(x) are (2x-1) and 6x³+25x²-24x+5 respectively.

if p(x)=2x²+9x-5,determine q(x)

tarinbansal

Use this formula->

edison

Thats right

If a and b are not both zero, the greatest common divisor of a and b can be computed by using least common multiple (lcm) of a and b:

$\operatorname{gcd}(a,b)=\frac{a\cdot b}{\operatorname{lcm}(a,b)}.$

Thus If GCD = HCF= (2x-1) and LCM = 6x³+25x²-24x+5

p(x)=2x²+9x-5, then q(x) is

q(x) = (2x-1) * ( 6x³+25x²-24x+5 ) / 2x²+9x-5

Now factorize the terms to get the results