Question

11. If a and B are zeroes of the polynomial x2 - 5x - k such that a- B = 1, then find the value of k​

Answer 1

Answer:

Given polynomial is x² - 5x - k

alpha and Beta are the zeros.

x² - 5x - k

In this polynomial,

a=1, b= -5, c= -k

alpha + beta = -b/a

= 5 .(i)

Given, alpha - beta = 1 .(ii)

From (i) & (ii)

beta = 2

alpha + beta = 5

alpha + 2 = 5

alpha = 3

alpha × beta = c/a

6 = -k/ 1

k = -6

Answer 2

Answer:

The value of the k is -6.

Step-by-step explanation:

Given: the polynomial is x²-5x-k

& a- B = 1 .

Find : The value of k.

Solution: As given, x²-5x-k

a and B are zeroes of the polynomial

Here, In this polynomial-

a = 1 , B = -5 , c = -k

As, a+B = -B/a

= -(-5)/1

= 5

=> a*B = c/a

= -k/1

= -k

As given , a-B = 1

now , square both sides

=> (a-B)²= (1) ( a²-B² = a²+B²-2aB)

=> a²+B²-2aB = 1

=> (a²+B²+2aB)- 4aB = 1 ( a²+B² =a²+B²+2aB)

=> (a+B)² - 4aB = 1

=> (5)² - 4(-k) = 1

=> 25+4k = 1

=> 4k = 1 - 25

=> 4k = - 24

=> k = - 6.