How do you find the discriminant and how many solutions does 2w^2 - 28w = -98 have?

May 10, 2015

Re writing the equation
$2 {w}^{2} - 28 w + 98 = 0$ , dividing by 2:
${w}^{2} - 14 w + 49 = 0$

formula for discriminant (D):
$D = {b}^{2} - 4 a c$

here:
$a = 1$ , $b = - 14$ and $c = 49$
(the coefficients of ${w}^{2}$ , $w$ and the constant term respectively)

finding $D$:
$D = {b}^{2} - 4 a c$
$D = \left(- {14}^{2}\right) - \left(4 \times 1 \times 49\right)$
$D = 196 - 196$
$D = 0$

formula for roots :
$w = \frac{- b \pm \sqrt{D}}{2 a}$
$w = \frac{14 \pm \sqrt{0}}{2 \times 1}$
$w = \frac{14 - 0}{2} = 7 \mathmr{and} \frac{14 + 0}{2} = 7$
$w = 7$

the equation has two real and equal roots as $D = 0$