Question

Find the zero of the polynomial

p(x)= 4x^2+24x+36​

Answer 1

$\bold{Answer}$

correct answer is α = -3 and β = -3

Step-by-step explanation:

4x^{2} + 24x + 364x2+24x+36

Here product = 36*4= 144

Sum = 12

By splitting the middle term we get :

4x^{2} +12x+12x+364x2+12x+12x+36                    12+12=24 and 12*12=144

Taking 4x and 12 as common factor we get:

4x(x+3) +12 (x+3)

(x+3) (4x+12)    

Therefore factors are : x + 3 and 4x + 12

α = -3 and β = -3

Answer 2

$Bonjour$

The equation is given to be : p(x) = 4x² + 24x + 36

To find the zeros of the given equation, Equate the given p(x) = 0

⇒ 4x² + 24x + 36 = 0

Dividing each term of the equation by 4

⇒ x² + 6x + 9 = 0

⇒ x² + 3x + 3x + 9 = 0

⇒ x( x + 3) + 3(x + 3) = 0

⇒ (x + 3)(x + 3) = 0

⇒ α = -3 and β = -3

Now, α + β = -3 - 3 = -6

-b/a = -24/4

⇒ -b/a = -6

So, α + β = -b/a

And, α·β = 9 = c/a

So, α·β = c/a