Question

if the roots of the quadratic equation x^2+MX+n=0 are tan 30 and tan 15, respectively, then find 2+n-m...​

Answer 1

Answer:

Given x

2

+px+q=0

From the given equation tan30

∘

+tan15

∘

=−p and tan30

∘

tan15

∘

=q

Now

tan(30

∘

+15

∘

)=

1−tan30

∘

tan15

∘

tan30

∘

+tan15

∘

⇒tan(45

∘

)=−

1−q

p

⇒1=−

1−q

p

⇒1−q=−p⇒q−p=1

⇒2+q−p=3