Question

Solve the following questions (Aly one)
1) In an A.P. second and fifth terms are the roots of the equations.
x2 - 4x - 32 = 0 find these numbers.
IE1​

Answer 1

The five terms of an A.P are -12, -8, -4, 0, 4.

Step-by-step explanation:

$x^{2} - 4x - 32 = 0\\=> x^{2} - 4x + 8x - 32 = 0\\=> x(x - 4) + 8(x - 4) = 0\\=> (x - 4)(x + 8) = 0\\=> x = -8, 4$

Second and fifth terms of A.P are -8 and 4.

Let the five terms of an A.P are (a - d), a, (a + d), (a + 2d), (a + 3d).

Second term = a = - 8

Fifth term = a + 3d = 4

=> -8 + 3d = 4

=> 3d = 4 + 8 = 12

=> d = $\frac{12}{3}$ = 4

Hence, a - d = -8 - 4 = -12

a = -8

a + d = -8 + 4 = -4

a + 2d = -8 + 2 x 4 = -8 + 8 = 0

a + 3d = -8 + 3 x 4 = -8 + 12 = 4

Hence, the five terms of an A.P are -12, -8, -4, 0, 4.