(4) Hey (3) Real and opposite sign ...
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# (4) Hey (3) Real and opposite sign 15. If 7 lies between the roots of the equ es between the roots of the equation 3x2 - 3 sin ax-2 cos2 a = 0 then a lies in the interval TTTT may have one root less than 2a

JEE/Engineering Exams
Maths
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( Q-15 ) - Houren expression: ( 3 x^{2}-(3 sin alpha) x-2 cos ^{2} alpha=0 ) 半 Now companing it with ( a x^{2}+b x+c=0 ), we get ( #+f(1)<0 ) because this equation is concave upwands [ therefore quad 3(1)^{2}-(3 sin alpha) 1-2 cos ^{2} alpha=0 quadlangle 0 ] ( left.Rightarrow 3-3 sin alpha-2 cos ^{2} alpha<0 quad text { (Use: } cos ^{2} alpha=1-sin ^{2} alpha, text { we get }right) ) [ Rightarrow quad 3-3 sin alpha-2left(1-sin ^{2} alpharight)<0 ] ( Rightarrow 2 sin ^{2} alpha-3 sin alpha+1<0 ) This is now a quadratic eque in sinialpha, solving it, we get: ( Rightarrow cdot sin ^{2} alpha-frac{3}{2} sin alpha+frac{1}{2}<0 ) March ( quad 2019 quad geqslant(sin alpha-1)left(sin alpha-frac{1}{2}right) mathbb{L} 0 ) ( overline{w_{k}} ) Mo Tu we Th Fr ( S_{a} S_{u} ) ( begin{array}{llllll}09 & & & 1 & 2 & 3 10 & 4 & 5 & 6 & 7 & 8 & 9 & 10end{array} ) for ( quad sin (t) sin frac{1}{2} ) of ( frac{90^{circ}}{A^{5}} cdot alpha<150^{circ} ) ( Rightarrow quad x in C ) ( Uleft(pi 2^{,} frac{5 pi}{6}right] )