Let a, b be integers such that all the roots of the equation (x2 + ax + 20)(a2 + 17x + b) = 0 are negative integers. What is the smallest possible value of a + b?
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
Let a, b be integers such that all the roots of the equation (x2 + ax + 20)(a2 + 17x + b) = 0 are negative integers. What is the smallest possible value of a + b?
Let a, b be integers such that all the roots of the equation (x2 + ax + 20)(a2 + 17x + b) = 0 are negative integers. What is the smallest possible value of a + b?
∵ Roots of (x2 + ax + 20)(a2 + 17x + b) = 0 are negative integers and we required (a + b)min
∴ a, b each should be minimum
a2 – 80 is perfect square and a is a positive integer
⇒ amin = 9
289 – 4b is a perfect square and b is a positive integer
⇒ bmin = 16 (using 8, 15, 17)
∴ (a + b)min = 25