Question

rs agarwal class 10 plynomial chapter ex 2c que. no. 21

Answer 1

since it is given that
alpha - beta = 1 (eq1)
from equation
alpha + beta = 5 (eq2)
(because alpha + beta = -b/a)
so by eq 1&2
2alpha = 6
alpha = 3
on putting the value of alpha in the given eq
(3)²-5×3+k=0
9-15+k=0
k=21

Answer 2

Let alpha denoted as a

and beta as b

So, it is given that

=>. a - b = 1 ....... ( i )

Now,


f ( x ) = x² - 5x + k


$sum \: of \: roots \: = \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$


=> a + b = 5. .....( ii )

Now,

adding ( i ) and ( ii )

a - b + a + b = 1 + 5

2a = 6

a = 3


Putting value of a in equation ( ii )

a + b = 5

3 + b = 5

b = 5 - 3

b = 2

Now,


$product \: of \: roots \: = \frac{constant \: term}{coefficient \: of \: {x}^{2} }$

=> ab = k/1

3 × 2 = k

6 = k