Questions
Consider equation . Which of the following is/are true?
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a
If 0<α<π4, then the equation has both roots in (sinα, cosα)
b
If π4<α<π2, then the equation has both roots in (sinα, cosα)
c
If 0<α<π4, then one root lies in (−∞, sinα) and the other in (cosα, ∞)
d
If π4<α<π2, then one root lies in (−∞, cosα) and the other in (sinα, ∞)
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Correct option is C
Let f(x)=(x−sinα)(x−cosα)−2.Then, f(sinα)=−2<0 and f(cosα)=−2<0.So, sinα and cosα lie between the roots.For 0<α<π4,sinα
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If the equation ax2 + bx + c = 0 (a > 0) has two real roots such that , then which of the following statements is/are true?
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