Question

Find the roots of the following quadratic equations, if they exist, by the method of completing the

square:

(iii) 4x^2+4 ✓3x+3=0​

Answer 1

$\large{\underline{\rm{\red{\bf{Given:-}}}}}$

Quadratic equation = $\sf 4x^{2}+4\sqrt{3}x+3=0$

$\large{\underline{\rm{\red{\bf{To \: Find:-}}}}}$

The roots of the following quadratic equations, if they exist, by the method of completing the  square.

$\large{\underline{\rm{\red{\bf{Solution:-}}}}}$

Converting the equation into $\sf a^{2}+2ab+b^{2}$, we get

$\implies \sf (2x)^{2} + 2 \times 2x \times \sqrt{3} + \sqrt{3}^{2} = 0$

$\implies \sf (2x + \sqrt{3} )^{2} = 0$

$\implies \sf (2x + \sqrt{3} ) = 0$ and $\sf (2x + \sqrt{3} ) = 0$

Therefore, either $\sf x=\dfrac{\sqrt{3} }{2}$ or $\sf x=\dfrac{\sqrt{3} }{2}$

$\large{\underline{\rm{\red{\bf{To \: Note:-}}}}}$

A polynomial of the form ax²+bx+c, where a,b and c are real numbers and a≠0 is called a quadratic polynomial.

When we equate a quadratic polynomial to a constant, we get a quadratic equation.

A quadratic equation can have two distinct real roots, two equal roots or real roots may not exist.