Question

14) zeroes of the polynomial x^2+5x+6 are...

Both positive
Both negative
One is positive and other is negative
None​

Answer 1

B) Both Negative

Explanation:

`(x^2+5x+6)\\=(x^2+2x+3x+6)\\=x(x+2) + 3(x+2)\\=(x+3)(x+2)\\Hence,\ as\ their\ factors\ are\ (x+3)\ and\ (x+2)\ their\ zeroes\ are\ (-3)\ and\ (-2)\ respectively..\\As\ they\ both\ are\ negative..\ the\ answer\ is\ b)\\\`

Answer 2

both negative

Explanation:

Descartes rule of signs tells us how many positive and negative real roots a polynomial has.

Given

f(x) = x² + 5x + 6 , with signs

+, +, + ← no change of signs, thus no positive zeros

f(- x) = (- x)² + 5(- x) + 6 = x² - 5x + 6 , with signs

+, -, + ← with 2 changes of signs. thus 2 negative zeros