Question

If one zero of polynomial x

2 + kx + 18 is double of the other, then k =

(a) 9 (b) ±3 (c) ±9 (d) 3​

Answer 1

Answer:

c) +/- 9

k = +/- 9

Step-by-step explanation:

Let the zeroes of the quadratic equation x^2 + kx + 18 be 'alpha' and 'beta'.

According to the question :

alpha = 2 beta

Then, we know that

(alpha) + (beta) = -b/a

=> 2beta + beta = -b/a

=> 3beta = -k/1

=> beta = -k/3 ....... (i)

Also we know that,

(alpha) × (beta) = c/a

=> (2beta) × (beta) = c/a

=> 2(beta^2) = 18/1 ..... (ii)

From equation (i) and (ii), we get

=> 2{(-k/3)^2} = 18

=> (k^2) /9 = 18/2

=> (k^2) /9 = 9

=> k^2 = 81

=> k = √81 = +/- 9

Hence,

k = +/- 9

Answer 2

pls check this attachement that i have given below ok