Question

zsquare -9z-36=0 solve by factorization method ​

Answer 1

Answer:

z= -3, 12

Step-by-step explanation:

You factor -36 into -12 and 3 because -12 + 3 = 9

and z^2 is just factored into z and z

so (z-12)(z+3)=0 and from there solve z-12=0 and z+3=0

and get z= 12 and -3

Answer 2

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• A polynomial
• Z²-9Z-36=0

${\sf{\green{\underline{\large{To\:Find}}}}}$

• Factors of the polynomial
• Relationship between cofficient

${\sf{\pink{\underline{\Large{Explanation}}}}}$

• Z²-9Z-36=0

• we have to spilt the middle term in such a way that the product become -36 and sum become -9z

Z²-9Z-36=0

=>Z²-9Z-36=0

=>Z²-12z+3z-36=0

=>Z(Z-12)+3(Z-12)=0

=>(Z-12) (Z+3) =0

=>Z=12,-3

Additional Information

Let the zeroes of the polynomial be$\tt\alpha{and}\beta$

Then,

$\rightarrow\tt\alpha{+}\beta{=}\frac{-b}{a}$

&

$\rightarrow\tt\alpha{\times}\beta{=}\frac{c}{a}$

Here,

a=1

b=-9

C=-36

☞

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{9}{1}$

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{Cofficient\:of\:Z}{Cofficient\:of\:Z^2}=$

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{-36}{1}$

$\rightarrow\tt{\large\alpha{\times}\beta{=}\dfrac{Constant\:term}{Cofficient\:of\:Z^2}}$

Hence,relation verified