Question

Find x, if g(x)=0 where
a) g(x)=5x-6÷7
b)g(x)=18-2x^2÷7
c) g(x)=6x^2+x-2

Answer 1

Solution:

(a)

Here, g(x) = (5x - 6)/7

Given, g(x) = 0

Then, (5x - 6)/7 = 0

or, 5x - 6 = 0

or, 5x = 6

or, x = 6/5

∴ the required solution is

x = 6/5

(b)

Here, g(x) = 18 - 2x²

Given, g(x) = 0

Then, 18 - 2x² = 0

or, 2x² - 18 =0

or, x² - 9 =0

or, x² - 3² = 0

or, (x + 3) (x - 3) = 0

Either x + 3 = 0 or, x - 3 = 0

i.e., x = - 3, 3

∴ the required solution is

x = - 3, 3

(c)

Here, g(x) = 6x² + x - 2

Given, g(x) = 0

Then, 6x² + x - 2 = 0

or, 6x² + (4 - 3) x - 2 = 0

or, 6x² + 4x - 3x - 2 = 0

or, 2x (3x + 2) - 1 (3x + 2) = 0

or, (3x + 2) (2x - 1) = 0

Either 3x + 2 = 0 or, 2x - 1 = 0

i.e., x = - 2/3, 1/2

∴ the required solution is

x = - 2/3, 1/2