Question

find the zero of the polynomial p(x)=4x^2+24x+36

Answer 1

$p(x) = 4x^{2} + 24x + 36$

To find the zeroes of the p(x)

p(x) = 0

$p(x) = 4x^{2} + 24x + 36 = 0$

Taking 4 as common

$\implies x^{2} + 6x + 9 = 0 \\ \implies x^{2} + 3x + 3x + 9 = 0 \\ \implies x(x + 3) + 3(x+3) = 0 \\ \implies (x+3)(x+3) = 0$

x + 3 = 0

x = -3

Therefore, zeroes of $p(x) = 4x^{2} + 24x + 36$ are -3 and -3.

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Polynomial: An expression which consists variable and coefficients involving expressions like addiction, subtraction etc.

Answer 2

Answer:

α = -3 and β = -3

Step-by-step explanation:

$4x^{2} + 24x + 36$

Here product = 36*4= 144

Sum = 12

By splitting the middle term we get :

$4x^{2} +12x+12x+36$                    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

Thanks