Question

Plz give me fupl answer

Answer 1

given zeroes :- 2-√3 and 2+√3

to make a polynomial :-

product of zeroes= (2-√3)(2+√3)= 2² - (√3)² = 4-3 = 1

sum of zeroes= 2+√3 + 2 - √3 = 4

f(x) = x² - ( sum of zeroes )x + ( product of zeroes)

now divide p(x)= x⁴ - 7x³ + 9x² + 13x - 4 with f(x)

so we get quotient = x² - 3x - 4 = q(x)

as when we divide a polynomial with its  factor then the quotient is also a factor of the respective polynomial.

therefore the the factors of q(x) will be same of p(x).

x² - 3x - 4

= x² - 4x + x - 4

= x(x-4)+1(x-4)

= (x+1)(x-4)

=> x = -1 and 4