Question

zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients X square + 7 x + 12​

Answer 1

Step-by-step explanation:

First of all finding the zeroes of the given polynomial p(x)

$p(x) = {x}^{2} + 7x + 12$

${x}^{2} + 4x + 3x + 12 = 0$

$x(x + 4) + 3(x + 4) = 0$

$(x + 3)(x + 4) = 0$

$x = ( - 4) \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: \: x = ( - 3)$

So -4 and -3 are the zeroes of the given polynomial.

here sum of the zeroes is -7 which is exactly equal to -b/a of the polynomial.

and, the multiply of the zeroes is also equal to c/a exactly.

Hence the relationship is verified.