Question
If sinθ and cosθ are the two roots to the equation 4x^2-5x+a=0, then the value of a should be (A)1/8 (B) 9/8 (C) −1/8 (D) −9/8 (E) 3/8
Answers
oobleck
Recall that for ax^2+bx+c=0,
the product of the roots is c/a
the sum of the roots is -b/a
so now you have
sinθ cosθ = a/4
sinθ + cosθ = 5/4
squaring, you get
sin^2θ + 2sinθ cosθ + cos^2θ = 25/16
1 + 2a/4 = 25/16
a = 9/8
the product of the roots is c/a
the sum of the roots is -b/a
so now you have
sinθ cosθ = a/4
sinθ + cosθ = 5/4
squaring, you get
sin^2θ + 2sinθ cosθ + cos^2θ = 25/16
1 + 2a/4 = 25/16
a = 9/8