Question

Find all the zeroes of the function f(x)=11x^2+x+5

Answer 1

Answer:

$x = \frac{1 + \sqrt{(-219)} }{22} , \space x = \frac{1 - \sqrt{(-219)} }{22}$

Step-by-step explanation:

f(x)=11x^2+x+5 is the given equation,

now comparing it with the  standard equation $ax^{2} + bx + c = 0$, we get

$11x^{2} + x + 5 = 0$

Here, a = 11, b = 1 and c = 5

Now  by QUADRATIC FORMULA

x =  $\frac{-b \pm \sqrt{b^{2} - 4ac} }{2a}$

Now, $b^{2} - 4ac = 1^{2} - 4 (11) (5) = 1 - 220 = -219$

Now as discriminant D < 0, then the roots are imaginary and distinct.

So, roots are $x = \frac{-1 + \sqrt{(-219)} }{22} , \space x = \frac{-1 - \sqrt{(-219)} }{22}$

These are the two roots of the given equation.