Question

Solve the equation 2x3

- 15x2 + 37x – 30 = 0, given that the roots of the

equation are in A.P.

Answer 1

Answer:

2, 2.5, 3 are in arithmetic progression

Explanation:

2x³-15x² + 37x–30 = 0

Given that a cubic equation.

We solve this cubic equation.

In order to solve cubic equation, we need to factorize this

Factor of given cubic equation are:

(x-2)(2x-5)(x-3)=0

Now

x-2 =0 ⇒ x= 2

2x-5 = 0 ⇒ x=5/2 ⇒ x = 2.5

x - 3 = 0 ⇒ x = 3

NOw roots are :

x = 2, 2.5, 3

Check that the roots are in arithmetic progression or not

common difference = 2.5 - 2 = 0.5

and 3 - 2.5 = 0.5

So, roots are in AP.

Answer 2

Answer:

Step-by-step explanation:

Sum of zeros=-b/a. 15/2

Product of zeros=-d/a. 30/2=15

(A+b)(a)(a-b)=(a²-b²)a

A+b+a+a-b=3a=15/2