Let P(x) be a polynomial with real coefficients, Let a,b∈R,a<b, be two consecutive roots of P(x) . Show that there exists c such that a≤c≤bandPprime(c)+100P(c)=0.
In the curve xayb=Ka+b , prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).
A curve is given by the equations x=sec2θ,y=cotθ˙ If the tangent at Pwhereθ=4π meets the curve again at Q,then[PQ] is, where [.] represents the greatest integer function, _________.
Two men PandQ start with velocity u at the same time from the junction of two roads inclined at 450 to each other. If they travel by different roads, find the rate at which they are being separated.