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.
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.
If x/12 − 3/x = 0, then the values of x are :
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