if the roots of the equation 2x^2-3x+5=0 are reciprocals of the roots of the equation ax^2+bx +2=0 then a and - Maths - Linear Inequalities

Question

if the roots of the equation 2x^2-3x+5=0 are reciprocals of the
roots of the equation ax^2+bx +2=0 then a and b are

Jegannathan Anandaraman · Answer

Hello Bhavya Patwa, the sum of zeros m + n = 3/2 and product of
zeros = m n = 5/2
The new quadratic has 1/m and 1/n as zeros
So sum (m+n)/m n = -b/a = 3/2 * 2/5 = 3/5
So -5b = 3a
Now product of zeros of new quadratic 1/mn = 2/a = 2/5
So a = 5 and b = -3
Let us verify now The new quadratic is 5 x^2 - 3 x + 2 = 0
So sum of zeros = 3/5 (verified) Product of zeros = 2/5 (verified)

if the roots of the equation 2x^2-3x+5=0 are reciprocals of the roots of the equation ax^2+bx +2=0 then a and b are