Question

alpha and bita are the zeroes of p(x) =x2-(k-6)x+(2k+1). Find the value of k if alpha + bita = alpha *bita

Answer 1

The given polynomial

P(x) = x^2 -(k-6)x + (2k+1)

There is a relation between the zeroes and the coefficients of the quadratic polynomial.

The relation between them is as follows :-

Let there be two zeroes for a quadratic polynomial. Say it alpha and beta
So,
Alpha + beta = -b/a

Alpha * beta = c/a


Now,
Applying similar conditions to given polynimal p(x)
We get that:-

Alpha + beta = -b/a = -{-(k-6)}/ 1
Alpha + beta = (k-6)

Alpha * beta = c/a = (2k+1)/ 1
Alpha * beta = (2k + 1)


Now,

Given that ,
Alpha + beta = alpha * beta

It means that

K-6 = 2k+1
Or, k - 2k = 1+6 =7
Or, (-k) = 7
OR,
K = (-7)

Answer 2

Answer:

The value ok k is 7

Step-by-step explanation:

sum of roots=product of roots.