If roots of equation x^2+px+q=0 are tan30 and tan15. then determine value of 2+q-p.
A)0
B)1
C)2
D)3

• tan30 and tan15 are roots of equation x^2+px+q=0
  
  then, tan30+ tan15= -p
  and tan30 * tan15= q
  
  HERE,
  tan45= tan(30+15)
  tan45= (tan30+tan15)/(1-tan30 * tan15)
  1 = -p/(1-q)
  1-q= -p
  1=q-p
  ADDING 2 BOTH SIDES THEN,
  2+1 = 2+q-p
  2+q-p = 3 ans
  
• 10 years agoHelpfull: Yes(1) No(0)
• D) 3
  
  x^2+px+q=0, roots are tan30 & tan15
  
  sum of roots = tan30 + tan15 = -p
  
  product of roots = tan30 * tan15 = q
  
  2+q-p
  = 2 + tan30 * tan15 + tan30 + tan15
  = 2 +( tan15 + tan30 + tan15*tan30 )
  = 2 + 1
  = 3
  -------------
  tan(30+15)= tan45 = (tan30 + tan15)/(1- tan30*tan15)
  => 1- tan30*tan15 = tan30 + tan15
  => tan15 + tan30 + tan15 * tan30 = 1
  
• 10 years agoHelpfull: Yes(1) No(0)
• 3
  
  A quadratic equation is of the form,
  x^2 - (sum of roots)x + (product of roots) = 0
  
  Here,
  Sum of roots = -p
  product of roots = q
  
  ie,
  tan 30 + tan 15 = -p
  tan 30*tan 15 = q
  
  2+q-p = 2+tan 30*tan 15 + tan 30 + tan 15
  =1 + (1+tan 15)(1+tan 30)
  = 1 + 2
  =3
  
  
• 10 years agoHelpfull: Yes(0) No(0)