Question

What are the solutions of 4x^2-x+9=0 ?

Answer 1

The answer is A

`x=(1+i√(143) )/(8)` and
`x=(1-i√(143) )/(8)`

Explanation:

∵ 4x² - x + 9 = 0 ⇒ is quadratic equation

∴
`x=\frac{-b+\sqrt{b^(2)-4ac } }{2a}`

∴
`x=\frac{-b-\sqrt{b^(2)-4ac } }{2a}`

Where a is the cooficient of x² , b is the cooficient of x and c is the numerical term

∵ a = 4 , b = -1 and c = 9

∴
`x=\frac{-(-1)+\sqrt{(-1)^(2)-4(4)(9) } }{2(4)} =(1+√(1-144) )/(8)`

`=(1+√(-143) )/(8)=(1+i√(143) )/(8)`⇒ i = √(-1)

∴
`x=(1-i√(143) )/(8)`

∴The solutions are:

x=
`(1+i√(143) )/(8)` and x=
`(1-i√(143) )/(8)`

Answer 2

Choice A is correct answer.

Explanation:

We have given a quadratic equation.

4x²-x+9 = 0

We have to find the solution of given equation.

We use following quadratic formula to find the solution.

x = (-b±√b²-4ac) / 2a

In given equation, a = 4 , b = -1 and c = 9

Putting given values in quadratic formula, we have

x = (-(-1)±√(-1)²-4(4)(9) ) / 2(4)

x = (1±√1-144) / 8

x = (1±√-143 ) / 8

x = (1±√-1√143) / 8 ∵ i = √-1

x = (1±√143i) / 8

hence,The solutions are (1+√143)/8 and (1-√143)/8.