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Question
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
Options
a2 + b2 + 2ac = 0
a2 – b2 + 2ac = 0
a2 + c2 + 2ab = 0
a2 – b2 – 2ac = 0
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Solution
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation a2 – b2 + 2ac = 0.
Explanation:
Given that sin θ and cos θ are the roots of the equation ax2 – bx + c = 0
So sin θ + cos θ = `b/a` and sin θ cos θ = `c/a`
Using the identity (sinθ + cos θ)2 = sin2θ + cos2θ + 2 sin θ cos θ
We have `b^2/a^2 = 1 + (2c)/a`
or a2 – b2 + 2ac = 0
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