Question

if 1 is a zero of the polynomial ay^2+ay+3 and y^2+y+b, then find the value of a and b ​

Answer 1

Let p(y) = ay² + ay + 3 and g(y) = y² + y + b

If 1 is the zero of p(y) and g(y) then,

p(y) = ay² + ay + 3

→ p(1) = a(1)² + a(1) + 3

→ 0 = a + a + 3

→ 0 = 2a + 3

→ 2a = -3

→ a = -3/2

g(y) = y² + y + b

→ g(1) = 1² + 1 + b

→ 0 = 1 + 1 + b

→ 0 = 2 + b

→ b = -2

Hence, a = -3/2 and b = -2

Good luck.