Question

If -1 and 3 are the roots of x2 + px + q = 0, find the values of p and q.

Answer 1

Answer:

Solution

Given equation is

x

2

+

p

x

+

q

=

0

Let

α

=

2

+

i

√

3

(given)

Then,

β

=

2

−

i

√

3

Now,

α

+

β

=

−

p

2

+

i

√

3

+

2

−

i

√

3

=

−

p

⇒

4

=

−

p

or

p

=

−

4

Also,

α

β

=

q

(

2

+

i

√

3

)

(

2

−

i

√

3

)

=

q

⇒

7

=

q

Hence, option 'C' is correct.