Question

ONLUI nseur
L. Solve the quadratic equation x2 – 12x + 32 = 0 by completing
square method :
2​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{x^2-12x+32=0}$

$\underline{\textbf{To find:}}$

$\textsf{The solution of the given quadratic equation}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{x^2-12x+32=0}$

$\textsf{This can be written as,}$

$\mathsf{x^2-12x=-32}$

$\textsf{Add 36 on botsides to make L.H.S. a perfect square}$

$\mathsf{x^2-12x+36=-32+36}$

$\mathsf{(x-6)^2=4}$

$\textsf{Taking square root on botsides, we get}$

$\mathsf{x-6=\pm\,2}$

$\mathsf{x=6\pm\,2}$

$\mathsf{x=6+2,\,6-2}$

$\implies\boxed{\mathsf{x=8,\,4}}$

$\therefore\textbf{Solutions are 4 and 8}$


$\underline{\textbf{Find more:}}$

Find the roots of the following quadratic (if they exist) by the method of completing the square.
√3x²+10x+7√3=0

Answer 2

Answer:

4,8 are the roots of the given quadratic equation

Step-by-step explanation:

By factorization method

Solution:

${x }^{2} - 12x + 32 = 0$

${x}^{2} - 4x - 8x + 32 = 0$

$x(x - 4) - 8(x - 4) = 0$

$(x - 4)(x - 8) = 0$

$x - 4 = 0 \: \: \: \: or \: \: \: \: x - 8 = 0$

$x = 4 \: \: \: \: \: or \: \: \: \: \: x = 8$

Ans. 4, 8 are the roots of the given quadratic equation.