Question

please answer18 question​

Answer 1

Answer:

Step-by-step explanation:

DEAR HUMAN BEING ,

p(x) = 2x^2 - 5x + 7

NOW , LET THE ZEROES OF THIS POLYNOMIAL BE α AND β ,  SO ,

SUM OF ZEROES = α + β = -b\a = 5\2   and  PRODUCT OF ZEROES = αβ =

                                                                                                           = c\a = 7\2

NOW , IN THE OTHER UNKNOWN POLYNOMIAL THE TWO ZEROES ARE :

(2α + 3β) AND (2β + 3α)      NOW ,

SUM OF ZEROES = (2α + 3β) + (2β + 3α) = 5 (α + β) = 5 * 5\2 = 25\2

PRODUCT OF ZEROES = (2α + 3β) (2β + 3α) = 13αβ + 6(α² + β²)

= 13αβ + 6((α + β)² - 2αβ) = 7αβ + 6(α+β)² = 7 * 7\2 + 6 * (5\2)² = 62

NOW ,

REQUIRED POLYNOMIAL = k( x²-(SUM OF ZEROES) + (PRODUCT OF

                                                                                            ZEROES))

                                           = (x² - 25\2x + 62) = 1\2(2x² - 25x + 124).

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