Question

if alpha and beta are the zeros of the polynomial p of x is equal to 6 x square + 5 x minus k find the relation alpha minus beta is equal to 1 by 6 also find the value of k​

Answer 1

Step-by-step explanation:

Given,

α and β are zeroes of polynomial

p(x)=6x^2+5x-k

Relation between zeroes and coefficients

sum of the zeroes (α+β)=(-b/a)

=(-5/6) ...........(1)

also,

α-β=1/6 ...(2)

On adding (1) and (2)

α+β=(-5/6)

α-β=(1/6)

___________

=>2α=-5/6+1/6

=>2α = [- 4/6]

=>α=[-1/3]

similarly, on subtracting (1)from(2)

α+β=(-5/6)

-[ α-β=(1/6)]

___________

=>2β=1/6+5/6

=>2β=6/6 or 1

=>β=1/2

now,

=>αβ=-k/6

=>(-1/3)×(1/2)=(-k/6)

=>(-1/6)= (-k/6)

=> (-k) = [-1/6×6]

=> k = 1

Therefore,value of K=1