Question

if one zero of the polynomial q(x) =x²+px+8 is double the other,then find the value of p and hence both zeroes of q(x) ​

Answer 1

Answer:

when p = 6, a = -2 and b = -4

OR

when p = -6, a = 2 and b = 4

Step-by-step explanation:

Let the zeroes be a(alpha) and b(beta)

Also a = 2b

b = a/2

We know that

a + b = -(coefficient of x)/(coefficient of x²)

a + b = -p/1

So, a + b = -p

(2b) + b = -p

3b = -p

b = -p/3----1

also,

a = -p - b

Also a × b = (constant term)/(coefficient of x²)

ab = 8/1 = 8

(2b)(b) = 8

2b² = 8

From eq.1 we get

2(-p/3)² = 8

p²/9 = 4

p² = 36

p = √36 = +6 or -6

b = -(6)/3 = -2 or -(-6)/3 = 2

a = -(6) - (-2) = -4 or -(-6) - 2 = 4

when p = 6, a = -2 and b = -4

OR

when p = -6, a = 2 and b = 4

Hope you understood it........All the best

Answer 2

Answer:

Roots are 2,4and p=-6 or Roots are -2,-4 and p=6