Question

Solve for the roots of the
quadratic equation
4x2 - 13x - 12 = 0 by
completing the square.​

Answer 1

Answer:

$4x^{2} - 13x - 12 = 0$

$(2x)^{2} - 2 (2x)(\frac{13}{4} ) + (\frac{13}{4} )^{2} - (\frac{13}{4} )^{2} - 12 =0$

$(2x-\frac{13}{4} )^{2} = \frac{169}{16} +12$

$(2x-\frac{13}{4} )^{2} = \frac{169+192}{16}$

$(2x-\frac{13}{4} )^{2} = \frac{361}{16}$

$(2x-\frac{13}{4} )^{2} = (\frac{19}{4})^{2}$

$Hence,$ $2x - \frac{13}{4} = \frac{19}{4}$

$2x = \frac{19}{4} +\frac{13}{4}$

$2x = \frac{32}{4}$

$2x = 8$

$x = 8/2$

$x = 4$

$2x - \frac{13}{4} = - \frac{19}{4}$

$2x = - \frac{19}{4}+ \frac{13}{4}$

$2x = - \frac{6}{4}$

$2x = - \frac{3}{2}$

$x = - \frac{3}{2}$ × $\frac{1}{2}$

$x = - \frac{3}{4}$

$Alpha = 4\\Beta = - \frac{3}{4}$

$Hope$ $it$ $helps$

Answer 2

guess this might help.