Question

$x {}^{2} - 14x + 120 = 0$
find the value of x by factarization method​

Answer 1

The first term is, x2 its coefficient is 1 .

The middle term is, -14x its coefficient is -14 .

The last term, "the constant", is -120

Step-1 : Multiply the coefficient of the first term by the constant 1 • -120 = -120

Step-2 : Find two factors of -120 whose sum equals the coefficient of the middle term, which is -14 .

-120 + 1 = -119

-60 + 2 = -58

-40 + 3 = -37

-30 + 4 = -26

-24 + 5 = -19

-20 + 6 = -14 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and 6

x2 - 20x + 6x - 120

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-20)

Add up the last 2 terms, pulling out common factors :

6 • (x-20)

Step-5 : Add up the four terms of step 4 :

(x+6) • (x-20)

Which is the desired factorization

Equation at the end of step 1 :

(x + 6) • (x - 20) = 0

Answer 2

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Correction:-

x²-14x-120=0

find the Value of x?

$\red{\boxed{\orange{\underline{\pink{\mathrm{Solution:-}}}}}}$

Write down the Equation↓

→x²-14x-120=0

In this equation, The middle term is considered as Sum of Equation and The Other 2 Side terms Are considered product of The Equation, On Simplifying them, We get

S=-14

P=-120

(-)20+6=-14

(-)20×6=-120

→x²-20x+6x-120=0

→x(x-20)+6(x-20)=0

•Taking (x+6)=0

→x+6=0

→x=-6

•Taking (x-20)=0

→x-20=0

→x=20

$\boxed{x=-6}$

Because if we put x=20 we wont get the Equation=0 but if we put x=-6 we Get the equation=0[LHS=RHS]