Question

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Find the quadratic polynomial whose zeros are (5-3√2) and (5+3√2) respectively

Answer 1

Answer:

given that,

zeros of a quadratic polynomial are (5 - 3 v2) and (5+3√2) respectively.

we know that,

when when the zeros of a qudratic polynomial are given

then,

quadratic equation

= x² - sum of zeros × x + product of zeros

here,

product of zeros = (5 - 3 v2)(5+3√2)

by the algebraic identity

a² - b² = (a + b)(a - b)

= 5² - (3√2)

= 25 - 18

= 7

sum of zeros = 5 - 3 √2 + 5+3√2

= 10

now,

we have,

product of zeros = 7

sum of zeros = 10

so,

quadratic polynomial = x² - 10x + 7

so,

The required polynomial will be

x² - 10x + 7