Let p(x)=x2-5x+a and q(x)=x2-3x+b, where a and b are positive integers Suppose hcf(p(x)q(x))=x-1 and k(x)=lcm(p(x)q(x)) if the - Maths - Relations and Functions

Question

​Let p(x)=x​2-5x+a and
q(x)=x2-3x+b, where a and b are positive integers
Suppose hcf(p(x)q(x))=x-1 and k(x)=lcm(p(x)q(x)) if the coefficient
of the highest degree term of k(x) is 1 , the sum of the roots of
(x-1)+k(x) is

Brijendra Pal · Accepted Answer

Hi, Since HCF of these two function is x-1 so it will satisfy the equation and hence x2-5x+a = 0 1-5+a = 0 a = 4 similarly, 1-3+b = 0 b = 2 Now kx= LCM of x2-5x+4 and x2-3x+2=lcm of  x2-4x-x+4 and x2-2x-x+2=LCM of  xx-4-1x-4 and xx-2-1x-2= x-4x-1 and x-2x-1= x-1x-4x-2Now x-1+kx= x-1+x-1x-4x-2=x-11+x2-6x+8=x-1x2-6x+9=x-1x-32So sum of roots = 1+3+3= 7 Regards=

​Let p(x)=x​2-5x+a and q(x)=x2-3x+b, where a and b are positive integers . Suppose hcf(p(x)q(x))=x-1 and k(x)=lcm(p(x)q(x)). if the coefficient of the highest degree term of k(x) is 1 , the sum of the roots of (x-1)+k(x) is

Let p(x)=x²-5x+a and q(x)=x²-3x+b, where a and b are positive integers . Suppose hcf(p(x)q(x))=x-1 and k(x)=lcm(p(x)q(x)). if the coefficient of the highest degree term of k(x) is 1 , the sum of the roots of (x-1)+k(x) is