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

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Answer 1 · 2015-05-10T18:33:26

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

formula for discriminant (D):
$D= b^2 - 4ac$

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

finding $D$ :
$D= b^2 - 4ac$
$D= (-14^2) - (4 xx 1 xx 49)$
$D= 196 - 196$
$D= 0$

formula for roots :
$w = (-b +- sqrt D) / (2a)$
$w = (14 +- sqrt 0) / (2 xx 1)$
$w = (14 - 0) / 2 = 7 and (14 + 0) /2 = 7$
$w = 7$

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

How do you find the discriminant and how many solutions does 2w^2 - 28w = -982w^2 - 28w = -98 have?