Q1 of 46 Page 1

If 1 is a root of the equations ay2 + ay + 3 = 0 and y2 + y + b = 0, then find the value of ab.

As 1 is the root of the equation, ay2 + ay + 3 = 0.

This means y = 1.


So by substituting y = 1 in the equation, we get


a(1)2 + a(1) + 3 = 0


⇒ a + a + 3 = 0


⇒ 2a + 3 = 0


⇒ 2a = -3


⇒ a = -3/2 …(i)


Also, 1 is the root of the equation y2 + y + b = 0


Substituting y = 1 in this equation, we get


(1)2 + (1) + b = 0


⇒ 1 + 1 + b = 0


⇒ 2 + b = 0


⇒ b = -2 …(ii)


As we have been asked to find ab, multiply equations (i) and (ii),


(a)(b) = (-3/2)(-2)


⇒ ab = 3


Hence, the value of ab is 3.


More from this chapter

All 46 →
2

In Fig. 1, the sides AB, BC and CA of a triangle ABC touch a circle at P, Q, and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, find the length of BC (in cm).

 3

In Fig. 2, a circle touches the side DF of ΔEDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm, calculate the perimeter of ΔEDF (in cm)

 4

If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle (in cm)

 5

Find the sum of the first 25 terms of an A.P. whose nth term is given by tn = 2 – 3n.