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 A and B respectively.
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.
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.
Find the value(s) of p for which the quadratic equation given as (p + 4) x² − (p + 1) x + 1 = 0 has real and equal roots. Also, find the roots of the equation(s) so obtained.
The sides of a right triangle are such that the longest side is 4 m more than the shortest side and the third side is 2 m less than the longest side. Find the length of each side of the triangle. Also, find the difference between the numerical values of the area and the perimeter of the given triangle.
Express the equation (x – 2)/(x – 3) + (x – 4)/(x – 5) = 10/3 ; (x ≠ 3, 5) as a quadratic equation in standard form. Hence, find the roots of the equation so formed.
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