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

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

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Answer 1 · 2015-05-10T18:33:26

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

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

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

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

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

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

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

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