Zsquare -9z-36=0 solve by factorization method

1.	Zsquare -9z-36=0 solve by factorization method
Answer» ✪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

Answer»

✪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

☞

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

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

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

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