Question

Find the zeros of the following quadratic polynomials and verify the relation between zeros and its coefficient f(x)=x^2+7x+12

Answer 1

The given polynomial is x2+7x+12. To find the zeroes of the given polynomial, equating the polynomial to 0, we have;
x2+7x+12 = 0⇒x2+4x+3x+12 = 0⇒x(x+4)+3(x+4) = 0⇒(x+3)(x+4) = 0⇒x = −3 and x = −4
Therefore -3 and -4 are the zeroes of the given polynomial.
And sum of the zeroes = -3 + (-4) = -7
and product of the zeroes = (−3)×(−4) = 12