Question

x^2-25x+84=0. Solve by factorization method Plz help me

Answer 1

Answer:

x=21,-4

Step-by-step explanation:

• x²-25x+84=0
• x²-21x-4x+84=0
• x(x-21)+4(x-21)=0
• (x-21)(x+4)=0
• (x-21)=0 (x+4)=0
• x= 21 x= -4

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Answer 2

✪AnSwEr

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

• A polynomial
• X²-25x+84=0

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

• Factors of the polynomial

Relationship between cofficient

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

X

we have to spilt the middle term in such a way that the product become -20 and sum become -x

X²-25x+84=0

=>X²-21x-4x+84=0

=>x(x-21)-4(x-21)=0

=>(x-4) (x-21)

=>x=4,21

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=-12

C=84

☞

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{12}{1}$

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

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{84}{1}$

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

Hence,relation verified