Question

2).Find the

zeroes of the polynomial x^2 +5x+6
the relationship between the zeroes and the coefficients.​

Answer 1

Answer:

Step-by-step explanation:

$x^2 +5x +6=0\\x^2 +2x +3x+6=0\\(x+3)(x+2)=0$

There fore the zeros are -3 and -2

Now the sum of zeros = -3 -2 = -5

and the product of zeros is = (-2)(-3)= 6.

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Answer 2

The zeroes of x²+5x+6 are -2 and -3

Given:

The quadratic polynomial :

x²+5x+6

Solution:

We know the method of splitting term.

Let's apply it here,

So,

→ x² + 2x + 3x + 6

→ x(x + 2) + 3(x + 2)

→ (x + 2)(x + 3)

Hence

The values of x² + 5x + 6 is zero when x + 2 = 0 Or x+3=0

•°• The zeroes of x²+5x+6 are -2 and -3.

___________________________

★ Verification :

i) The sum of the Zeroes = - 2 + (- 3)

→ -5

→ (- 5)/1

$= \sf \dfrac{Coefficient\:of\; x}{Coefficient \:of\:x^2}$

ii) Product of the zeroes

→ (-2)(-3)

→ 6

→6/1

$= \sf \dfrac{Constant \: term}{Coefficient \:of\:x^2}$