Question

If roots of the quadratic equation mx^2-nx+k=0 are tan 33 and tan 12 find value of 2m+n+k/m

Answer 1

Step-by-step explanation:

Given If roots of the quadratic equation mx^2-nx+k=0 are tan 33 and tan 12 find value of 2m+n+k/m

• Now given quadratic equation is mx^2 – nx + k = 0
• So comparing the given equation with ax^2 + bx + c = 0 we get  
• So a = m , b = - n and c = 1
• So sum of roots α + β = - b/a = - (- n) / m = n/m
• Product of roots = αβ = c/a = k/m
• So the roots are tan 33 and tan 12 , so we get
• So tan 33 + tan 12 = n/m --------------1
• Also, tan33 tan 12 = k/m ---------------2
• Now we can write 2m + n + k = 2m/m + n/m + k/m
•                                                   = 2 + tan 33 + tan 12 + tan33 tan 12 ---------3
•                     We have tan (33 + 12) = tan 45
•                           Or tan 33 + tan 12 / 1 – tan 33 tan 12 = 1 (using tan (A + B) )
•                         So tan 33 + tan 12 = 1 – tan 33 tan 12
•                      Or tan 33 + tan 12 + tan 33 tan 12 = 1
•            Substituting this value in equation 3 we get
•                                               = 2 + 1
•                                            = 3
•     Therefore we get 2m + n + k / m = 3

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