Math, asked by Mehekjain, 1 year ago

Factors of : x^2 - 7 x + 1

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Answers

Answered by mia76

Answer:

x2-7x-1

Final result :

x2 - 7x - 1

Step by step solution :

Step 1 :

Trying to factor by splitting the middle term

1.1 Factoring x2-7x-1

The first term is, x2 its coefficient is 1 .

The middle term is, -7x its coefficient is -7 .

The last term, "the constant", is -1

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

Step-2 : Find two factors of -1 whose sum equals the coefficient of the middle term, which is -7 .

-1 + 1 = 0

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

x2 - 7x - 1

Answered by BRAINLYBOOSTER12

$\huge\boxed{\underline{\mathcal{\red{A}\green{\:N}\pink{S}\orange{W}\blue{E}\pink{R}}}}\: :$

USE QUADRATIC FORMULA TO PROCEED THIS QUESTION !

x² - 7x + 1 is a second degree polynomial.

If carefully, calculated we will see that the polynomial admits two roots :

$\frac{7 + \sqrt{45} }{2} \: \: and \: \:\frac{7 - \sqrt{45} }{2}$

Therefore, the factors can be

$(x - \frac{7 + \sqrt{45} }{2} )(x - \frac{7 - \sqrt{45} }{2} )$

Hence, x² - 7 x + 1 = $(x - \frac{7 + \sqrt{45} }{2} )(x - \frac{7 - \sqrt{45} }{2} )$

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