Question

if sinA+cosA=1/5, then a value of tanA/2 satisfies which of the equation?
a. 2x^2-x-1
b.x^2-2x-3=0
c.2x^2-5x-3=0
d. 2x^3-7x^2+2x+3=0

Answer 1

sinA+cosA=1/5
square both sides
sin^2A + 2sinAcosA + cos^2A = 1/25
2sinAcosA = 1/25 - 1 = -24/25
sin 2A = -24/25

setting my calculator to radians
2A = 4.4286 or 2A = 4.9962
A/2 = 1.10715 or A/2 = 1.249

so tan A/2 = 3.99999 or tan A/2 = 3
or tan A/2 = 0

clearly 0 does not work as a zero for any of the given equations, (they all have a constant)

tan A/2 = 3 does work in equation b)
which would factor to (x-3)(x+1) = 0 to get a root of 3
3 is also a root of c) and d) since they both factor containing a factor of (x-3)

( I know I should have been able to get tan A/2 = 3 without relying on my calculator,