Question

The sum of the zeroes ofthe polynomial 2x -x-1 is




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Answer 1

Answer:

a = 2, b = -1, c= -1

2x²- x-1

= 2x²-2x+x-1

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

(x-1) (2x+1)

x= 1 , -1/2

let alpha be 1 and beta be -1/2

sum of zeros = - b/a

= -(-1)/2

=1/2.

Step-by-step explanation:

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Answer 2

Question :

Correct question - The sum of the zeroes of the polynomial 2x²-x-1 is

Answer :

 Sum of zeroes = 1/2

Given :

polynomial, 2x² - x - 1

To find :

Sum of zeroes

Solution :

We can find the sum of zeroes in two methods.

• Relationship between zeroes and coefficients
• Finding the zeroes and adding them.

RELATIONSHIP BETWEEN ZEROES AND COEFFICIENTS :

 

  Given polynomial,

    2x²-x-1

>> It is of the form ax² + bx + c

     a = 2,b = -1,c = -1

 where

a - coefficient of x²

b - coefficient of x

c - constant term

>>> Sum of zeroes = -b/a = -(x coefficient)/x² coefficient

                                 = -(-1)/2

                                 = 1/2

>>> Product of zeroes = c/a = constant term/x² coefficient

                                      = -1/2

FINDING THE ZEROES :

        By sum-product pattern,

>> Find the product of quadratic term [ax²] and constant term [c]

    = 2x² × (-1 )

    = -2x²

>> find the factors of "-2x²" in pairs

    $=> -2x \times x \\\\ => 2x \times -x$

 

>> From the above, find the pair that adds to get linear term [bx]

      -2x + x = -x

>> So, split 3x as -2x and x

  2x² + 3x - 1 = 0

 2x² - 2x + x - 1 = 0

>> Find the common factor

    2x(x - 1) + 1(x - 1) = 0

      (x - 1) (2x + 1) = 0

=> x - 1 = 0 ; x = +1

=> 2x + 1 = 0 ; x = -1/2

∴ 1 and -1/2 are the zeroes of the polynomial.

⇒ SUM OF ZEROES = 1 + (-1/2)

                                   = 1 - 1/2

                                   = (2-1)/2

                                   = 1/2