The zeroes of the polynomial x2+5x+6 are :
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Step-by-Step Solution
Step 1: Set the polynomial to zero
To find the zeroes of a polynomial, we set the polynomial equal to zero. This gives us a quadratic equation that we need to solve for x.
Step 2: Factor the quadratic equation
We need to find two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of the x term). These numbers are 2 and 3. So, we can factor the quadratic equation as (x+2)(x+3)=0.
Step 3: Solve for x
For the product of two factors to be zero, at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x. This gives us the two zeroes of the polynomial.