Question

Find the smallest value of p for which the quadratic equation x² – 2(p + 1)x + p² = 0 has real roots. Hence, find the roots of the equation so obtained.

Find the zeroes of the polynomial q(x) = 8x² – 2x – 3. Hence, find a polynomial whose zeroes are 2 less than the zeroes of q(x).

There is a circular park of diameter 65 m as shown in the following figure, where AB is a diameter. An entry gate is to be constructed at a point P on the boundary of the park such that distance of P from A is 35 m more than the distance of P from B. Find distance of point P from points A and B respectively.

A 2-digit number is seven times the sum of its digits and two (2) more than 5 times the product of its digits. Find the number.