How do you find the discriminant and how many and what type of solutions does #x^2-8x+16=0# have?

Answer 1

The equation is of the form #color(blue)(ax^2+bx+c=0# where:

#a=1, b=-8, c=16#

The Disciminant is given by : #Delta=b^2-4*a*c# # = (-8)^2-(4*1*16)# # = 64-64=0#

If #Delta=0# then there is only one solution. (for #Delta>0# there are two solutions, for #Delta<0# there are no real solutions)

As #Delta = 0#, this equation has ONE REAL SOLUTION

As #Delta = 0#, #x = -b/(2a) = -(-8)/(2*1) = 8/2 = 4#

#x = 4# is the solution

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Answer 2

Kennedy Adams

The discriminant of a quadratic equation ( ax^2 + bx + c = 0 ) is given by the formula ( D = b^2 - 4ac ). For the equation ( x^2 - 8x + 16 = 0 ), the discriminant is ( D = (-8)^2 - 4(1)(16) = 64 - 64 = 0 ). Since the discriminant is equal to zero, the quadratic equation has two real and equal solutions.

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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.