cube root less than 1 min #youtubeshorts

If alpha,beta are the roots of the equation x^(2)-2p(x-4)-15=0 then the set of values of p for which one root is less than 1 and the other root is greater than 2 is

If bgta then show that the equation (x-a)(x-b)-1=0 has one root less than a and other root greater than b.

Out of the two roots of x^(2)+(1-2 lambda)x+(lambda^(2)-lambda-2)=0 one root is greater than 3 and the other root is less than 3 ,then the limits of lambda are

Out of the two roots of x^(2)-2 lambda x+lambda^(2)-1=0 one is greater than 4 and the other root is less than 4, then the limits of lambda are

The square root of a positive number less than 100 lies between: