Question

Find the range of x for the given inequality :-

5x < 2 - 3x²​

Answer 1

Answer:

The inequality can be separated into two parts.

3x - 2 < 10 + x ----------- eqn(1)

10 + x < 2 + 5x ------------ eqn(2)

From eqn(1), collect like terms:

3x - x < 10 + 2

2x < 12

divide both sides by 2

x < 6 ----------- eqn(3)

Similarly, from eqn(2), collect like terms,

10 - 2 < 5x - x

8 < 4x

dicide both sides by 4

2 < x ------------- eqn(4)

combining eqn(3) and eqn(4),

2 < x < 6

Answer 2

Answer:

Required Factors = (5x + 2)(x - 1)

SoluTion:

Given Polynomial :

5x² - 3x - 2 = 0

We've to factorise the given Polynomial.

Product = -10

Sum = -3

Factors = (-5,2)

By splitting middle term,

→ 5x² - 5x + 2x - 2 = 0

→ 5x (x - 1) +2 (x - 1) = 0

→ (5x + 2)(x - 1) = 0

We get,

x = \dfrac{-2}{5}

5

−2

and 1.