Polynomials (C10)

Find the zeroes of the quadratic polynomial x2 + 7x + 10, and verify the relationship between the zeroes and the coefficients.

Solution

x2 + 7x + 10 = (x + 2)(x + 5)

So, the value of x2 + 7x + 10 is zero when x + 2 = 0 or x + 5 = 0

Therefore, the zeroes of x2 + 7x + 10 are –2 and –5.

Sum of zeroes = -7 = –(Coefficient of x) / (Coefficient of x2)

Product of zeroes = 10 = Constant term / Coefficient of x2