What are the zeroes of f (x) = x2 + 5 x + 6 ?
The zeroes of a polynomial are the values that make the polynomial zero as a whole.
Answer: The zeroes of the function f (x) = x2 + 5 x + 6 is x = - 2 and x = - 3.
Let's find the zeroes of the polynomial.
To find the zeroes of the quadratic equation, we will put the value of the function equal to zero.
⇒ x2 + 5 x + 6 = 0
We will factorize the quadratic equation by splitting the middle term.
⇒ x2 + 2x + 3 x + 6 = 0
⇒ x (x + 2) + 3 (x + 2) = 0
⇒ (x + 2) (x + 3) = 0
Put both the values equal to zero.
⇒ (x + 2) = 0 and (x + 3) = 0
⇒ x = - 2 and x = - 3
Hence, we have two values of x that make the value of the polynomial equal to zero.
You can verify your answer using Cuemath's online Roots of Quadratic Equation Calculator.