Question

OR
Find the roots of the following quadratic equation by applying the quadratic formula
4x square+4root 3x +1=0​

Answer 1

Answer:

-√3+√2/2 , -√3-√2/2

Step-by-step explanation:

Given,

4x² + 4√3x + 1 = 0

To Find :-

Roots of the quadratic equation by the quadratic formula.

How To Do :-

By comparing the given quadratic equation with general Form of quadratic equation we will get the values of a , b , c then we need to substitute those in quadratic formula to find the roots of the quadratic equation.

Formula Required :-

If ' ax² + bx + c = 0' is the general form of quadratic equation then the roots of the quadratic equation are :-

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

Solution :-

Comparing 4x² + 4√3x + 1 = 0 with general form of quadratic equation ax² + bx + c = 0 :-

→ a = 4 , b = 4√3 , c = 1

Substituting in the formula :-

$x=\dfrac{-4\sqrt{3}\pm\sqrt{(4\sqrt{3})^2-4(4)1}}{2(4)}$

$=\dfrac{-4\sqrt{3}\pm\sqrt{16(3)-16}}{8}$

$=\dfrac{-4\sqrt{3}\pm\sqrt{48-16}}{8}$

$=\dfrac{-4\sqrt{3}\pm\sqrt{32}}{8}$

$=\dfrac{-4\sqrt{3}\pm4\sqrt{2}}{8}$

$=\dfrac{4(-\sqrt{3}\pm\sqrt{2})}{8}$

$=\dfrac{-\sqrt{3}\pm\sqrt{2}}{2}$

$=\dfrac{-\sqrt{3}+\sqrt{2}}{2},\dfrac{-\sqrt{3}-\sqrt{2}}{2}$

∴ Value of 'x' = -√3+√2/2 , -√3-√2/2