Question

31. Ifa and B are the zeros of he polynomial x2 - 5x + k such that alpha- Beta= 1, find the value
of k​

Answer 1

let alpha and beta are zeroes of given polynomial

We know that alpha +beta= -b/a

alpha + beta= -5/1

alpha +beta= -5......eq1

alpha-beta=1......eq2

using elimination method ,

alpha-beta=1

+ alpha +beta= -5

so we find

2alpha= -4

alpha= -2

putting alpha = -2 in given polynomial

so,x= -2

p(x)=x²+5x+k

let p(x)=0

0=x²+5x+k

0= -2²+5(-2)+k

0= 4-10+k

0= -6+k

6=k

k=6

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Answer 2

Answer:

k = 6

Step-by-step explanation:

alpha and beta are zeros of the polynomial f(x) = x^2 - 5x+k

let alpha = a beta = b

a+b = (-5/1)= 5; ab = k/1 = k

now a -b =1

squaring both sides

(a-b)^2=1

(a+b)^2-4ab-1

25-4k = 1

4I = 24

k= 6