Question

Following is cubic polynomial with their zeroes. Verify the relationship between all zeroes and the coeff
2x3 + x2 – 5x + 2; 2, 1, - 2​

Answer 1

Question :

Following is cubic polynomial with their zeroes. Verify the relationship between all zeroes and the coeff icients

2x3 + x2 – 5x + 2; 1/2, 1, - 2              

[ mistake in your question, the zeroes are 1/2,1,-2]

Answer :

Given :

 Cubic polynomial, 2x³ + x² - 5x + 2

 zeroes of this polynomial = 1/2,1,-2

To verify :

 Relationship between zeroes and coefficients

Solution :

  Given cubic polynomial, 2x³ + x² - 5x + 2

  It is of the form ax³+ bx² + cx + d

  ∴ a = 2, b = 1, c = -5, d = 2

  ⇒ coefficient of x³ = a

      coefficient of x² = b

      coefficient of x = c

      constant term  = d

RELATIONSHIP BETWEEN ZEROES AND COEFFICIENTS :

⇒ Sum of zeroes = 1/2 + 1 + (-2)

                              = 3/2 - 2

                              = (3-4)/2

                              = -1/2

                              = -b/a

                              = -x² coefficient/x³ coefficient

⇒ Sum of the product of zeroes taken two at a time

           = (1/2)(1) + (1)(-2) + (-2)(1/2)

           = 1/2 - 2 - 1

           = 1/2 - 3

           = (1-6)/2

           = -5/2

           = c/a

           = coefficient of x/x³ coefficient

⇒Product of zeroes = (1/2)(1)(-2)

                                   = -2/2

                                   = -d/a

                                   = - constant term/x³ coefficient      

                                       

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