How do you find the zeros, if any, of #y= -x^2 -3x +17 #using the quadratic formula?

Answer 1

#x=-3/2+-sqrt77/2# are the two zeros

You would solve the equation #-x^2-3x+17=0#

Let's apply the quadratic formula:

#x=(-b+-sqrt(b^2-4ac))/(2a)#
#x=(3+-sqrt(9-4(-1)*17))/-2#
#=(3+-sqrt(77))/-2#
#=-3/2+-sqrt77/2#
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Answer 2

To find the zeros of the quadratic function ( y = -x^2 - 3x + 17 ) using the quadratic formula:

  1. Identify the coefficients ( a = -1 ), ( b = -3 ), and ( c = 17 ).
  2. Substitute these values into the quadratic formula: ( x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} ).
  3. Calculate the discriminant, ( b^2 - 4ac ).
  4. If the discriminant is positive, there are two real roots. If it's zero, there's one real root (a repeated root). If it's negative, there are no real roots (two complex roots).
  5. Substitute the values of ( a ), ( b ), and ( c ) into the quadratic formula and solve for ( x ).

The quadratic formula is:

[ x = \frac{{-(-3) \pm \sqrt{{(-3)^2 - 4(-1)(17)}}}}{{2(-1)}} ]

[ x = \frac{{3 \pm \sqrt{{9 + 68}}}}{{-2}} ]

[ x = \frac{{3 \pm \sqrt{{77}}}}{{-2}} ]

Therefore, the zeros of the function are:

[ x = \frac{{3 + \sqrt{{77}}}}{{-2}} ] and [ x = \frac{{3 - \sqrt{{77}}}}{{-2}} ]

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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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