Vardaan Learning Institute

Q12. Which of the following equations does not have a real root?

• (A) \(x^2 = 0\)
• (B) \(2x - 1 = 3\)
• (C) \(x^2 + 1 = 0\)
• (D) \(x^3 + x^2 = 0\)

Q35 (a). There is a circular park of diameter 65 m where AB is a diameter. An entry gate is to be constructed at a point P on the boundary 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.

Q35 (b). Find the smallest value of \(p\) for which the quadratic equation \(x^2 - 2(p+1)x + p^2 = 0\) has real roots. Hence, find the roots.