Question

If a polynomial 8x^4-8x^3-18x^2 -px-q is exactly divisible by 4x^2-4x+1 then find the value of p and q

Answer 1

• 1 equation.(8x^4-8x^3-18x^2-px-q) is exactly divi sible by 2.equation 4x^2-4x+1
• it means that roots of 4x^2-4x+1 is also roots of 1st equation
• factor of 2nd equation is (2x-1)^2
• means it have repeated root x=1/2
• Concept- important thing is that if there is repeated roots then it also satisfy the derivative of given first equation.
• puting x=1/2 in 1st equation
• 8×1/16-8×1/8-18/4-p×1/2-q=0
• from this we get
• p+2q=-10. -3eqation
• puting x=1/2 in the derivative of 1 st equation
• derivative of 1st equation
• 32x^3-24x^2-36x-p=0
• 32×1/8-24×1/4-36×1/2-p=0
• p=-20
• putting value of p in 3rd equation we get q=5
• hence p=-20 &q=5

Answer 2

Answer:

Your answer :))

Thank you!!