Question

X2-x+2 factorize this equation...the question is correct

Answer 1

Correct Question

• X²-x-2

✪AnSwEr

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

• A polynomial
• X²-x-2

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

Factors of the polynomial

Relationship between cofficient

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

X²-X+2

we have to spilt the middle term in such a way that the product become 2 and sum become -x

X²-X-2

=>X²-2x+x-2

=>x(x-2)+1(x-2)

=>(x+1) (x-2)

=>x=-1,2

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=-1

C=-2

☞

$\rightarrow\tt\alpha{+}\beta{=}\dfrac{-(1)}{1}$

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

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{-2}{1}$

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

Hence,relation verified

Answer 2

QUESTION:

${x}^{2} - x - 2$

$\red {(correct \: question)}$

Factorised it.

ANSWER:

Quadratic equation is in the form of

$a {x}^{2} + bx + c = 0$

In order to find the zeroes. we have to factorised it,

Step 1 :

Split the middle term in such a way that it's sum equal to b i.e. -1 and product equal to a ×c that is 2.

${x}^{2} - 2x + x - 2$

Step 2 :

Taking common factor

$x(x - 2) + 1(x - 2)$

$(x + 1)(x - 2)$

so,

$x + 1 = 0 \\ x = - 1$

or

$x - 2 = 0 \\ x = 2$

FINAL ANSWER :

$\huge\red{- 1 \: and \: 2 \: are \: the \: zeroes}$

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