If sinθ,cosθ are the roots of 6x2−px+1=0 , then p2 =

The given quadratic equation is 6x2−px+1=0  …. ( 1 ) sinθ,cosθ  are the roots of given Eq. ( 1 )⇒ sum of the roots : sinθ+cosθ=p6,  Product of the roots : sinθcosθ=16 Take sinθ+cosθ=p6 Squaring on both sides and simplify, we get ⇒sin2θ+cos2θ+2sinθcosθ=p236       ⇒1+2(16)=p236        (∵ sin2θ+cos2θ=1) ⇒ p2=48