Question

5. Find the discriminant of 15x2 = 4x – 1 and describe

the nature of the roots of the equation. Then solve the
equation by using the Quadratic Formula.

Answer 1

a) The discriminant of the equation = - 44

b)The nature of the roots will be imaginary.

c)
`x = (2 +√(11) i)/(15)  or, x = (2 - √(11) i)/(15)`

Explanation:

Here, the given expression is
`15x^(2)  = 4x -1`

or,
`15x^(2)  -  4x + 1   = 0`

Now the discriminant (D) of a quadratic equation
`ax^(2)  +b x + c   = 0`

D =
`b^(2)   -  4ac  = (-4)^(2)  -  4(15) (1)  = 16 - (60) = -44`

Hence, the discriminant of the equation = - 44

As D< 0, so the roots will be imaginary.

Now,by quadratic formula :
`x = \frac{-b \pm \sqrt{b^(2)  - 4ac} }{2a}`

So, here
`x = (-(-4) \pm √(D) )/(2a)  = (4 \pm √((-44 )) )/(30)`

So, either
`x = (4 + √((-44 )) )/(30) or, x =  (4 - √((-44 )) )/(30)`

or,
`x = (2 +√(11) i)/(15)  or, x = (2 - √(11) i)/(15)`