Question

If x and y are zeroes of the polynomial f(x)=2x^2-5x+7. Find the polynomial whose zeroes are 2x+3y&3x+2y .

Answer 1

Answer:

Step-by-step explanation:

polynomial whose zeroes are 2x+3y&3x+2y .

(k - (2x+3y))(k -(3x +2y))= 0

k^2 - k(5x +5y) + (6x^2 + 6y^2 + 13xy) = 0

k^2 -5k(x+y) + 6(x^2 + y^2 + 2xy) + xy = 0

k^2 -5k(x+y) + 6(x + y)^2 + xy = 0

x and y are zeroes of polynominal 2x^2 -5x + 7 = 0

x + y = 5/2

xy = 7/2

putting these values in above equation

k^2 -5k(5/2) + 6(5/2)^2 + 7/2 = 0

k^2 -25k/2 + 6(25/4)+ 7/2 = 0

k^2 -25k/2 + 75/2 +7/2 = 0

k^2 - 25k/2 + 82/2 = 0

2k^2 - 25k + 82 = 0

f(x)= 2x^2 -25x + 82