Question

if alpha and beta are the zeros of the polynomial P of x = 2 X square + 5 x plus k stratifying the relationship Alpha square + beta square + alpha beta = 21 by 4

Answer 1

Answer:

Given polynomial p(X)=2x^2+5x+k

Here a=2 ,b=5 , c=k

Alpha+beta= -b/a = -5/2

Alpha×beta= c/a = k/2

Alpha square + beta square+ alpha×beta= 21/4

(Alpha + beta)^2 - 2alpha×beta + alpha×beta= 21/4

(Alpha+beta)^2 - alpha×beta = 21/4

(-5/2)^2 - (k/2) = 21/4

-k/2 = 21/4 - 25/4

-k/2 = -4/4

-k/2 = -1

-k = -2

K=2 Answer

Answer 2

Step-by-step explanation:

Alpha+beta= -b/a = -5/2

Alpha+beta= -b/a = -5/2Alpha×beta= c/a = k/2

Alpha+beta= -b/a = -5/2Alpha×beta= c/a = k/2Alpha square + beta square+ alpha×beta= 21/4

Alpha+beta= -b/a = -5/2Alpha×beta= c/a = k/2Alpha square + beta square+ alpha×beta= 21/4(Alpha + beta)^2 - 2alpha×beta + alpha×beta= 21/4

Alpha+beta= -b/a = -5/2Alpha×beta= c/a = k/2Alpha square + beta square+ alpha×beta= 21/4(Alpha + beta)^2 - 2alpha×beta + alpha×beta= 21/4(Alpha+beta)^2 - alpha×beta = 21/4

Alpha+beta= -b/a = -5/2Alpha×beta= c/a = k/2Alpha square + beta square+ alpha×beta= 21/4(Alpha + beta)^2 - 2alpha×beta + alpha×beta= 21/4(Alpha+beta)^2 - alpha×beta = 21/4(-5/2)^2 - (k/2) = 21/4

Alpha+beta= -b/a = -5/2Alpha×beta= c/a = k/2Alpha square + beta square+ alpha×beta= 21/4(Alpha + beta)^2 - 2alpha×beta + alpha×beta= 21/4(Alpha+beta)^2 - alpha×beta = 21/4(-5/2)^2 - (k/2) = 21/4-k/2 = 21/4 - 25/4

Alpha+beta= -b/a = -5/2Alpha×beta= c/a = k/2Alpha square + beta square+ alpha×beta= 21/4(Alpha + beta)^2 - 2alpha×beta + alpha×beta= 21/4(Alpha+beta)^2 - alpha×beta = 21/4(-5/2)^2 - (k/2) = 21/4-k/2 = 21/4 - 25/4 -k/2 = -4/4

Alpha+beta= -b/a = -5/2Alpha×beta= c/a = k/2Alpha square + beta square+ alpha×beta= 21/4(Alpha + beta)^2 - 2alpha×beta + alpha×beta= 21/4(Alpha+beta)^2 - alpha×beta = 21/4(-5/2)^2 - (k/2) = 21/4-k/2 = 21/4 - 25/4 -k/2 = -4/4-k/2 = -1

Alpha+beta= -b/a = -5/2Alpha×beta= c/a = k/2Alpha square + beta square+ alpha×beta= 21/4(Alpha + beta)^2 - 2alpha×beta + alpha×beta= 21/4(Alpha+beta)^2 - alpha×beta = 21/4(-5/2)^2 - (k/2) = 21/4-k/2 = 21/4 - 25/4 -k/2 = -4/4-k/2 = -1 -k = -2

K=2