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

Answer 1
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#
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Answer 2

To find the discriminant of the quadratic equation (2w^2 - 28w = -98), use the formula for the discriminant, which is (b^2 - 4ac), where (a), (b), and (c) are the coefficients of the quadratic equation.

For this equation: (a = 2), (b = -28), (c = -98).

Plug these values into the discriminant formula:

[\text{Discriminant} = (-28)^2 - 4(2)(-98)]

[\text{Discriminant} = 784 + 784]

[\text{Discriminant} = 1568]

Since the discriminant is positive (1568), there are two distinct real solutions for the quadratic equation.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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