How do you find the roots, real and imaginary, of #y=-2(x+1)^2-(x-3)^2-10 # using the quadratic formula?

Answer 1

#color(blue)(x = (1 - isqrt62)/3, (1 + i sqrt62) / 3#

#y = -2(x+1)^2 - (x-3)^2 - 10#
#y = -2x^2 - 4x - 2 -x^2 + 6x - 9 - 10#
#y = -3x^2 + 2x - 21#
#a = -3, b = 2, c = =-21#
#x = (-b +- sqrt(b^2 - 4ac)) / (2a)#
#x = (-2 +- sqrt(4 - 252)) / - 6#
#color(blue)(x = (1 - isqrt62)/3, (1 + i sqrt62) / 3#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the roots of (y = -2(x+1)^2 - (x-3)^2 - 10), we first simplify the equation. Then, we can identify the coefficients and apply the quadratic formula. However, it's worth noting that this equation isn't in standard quadratic form. Instead, we can expand and rearrange it to resemble a quadratic equation before proceeding with the quadratic formula.

[ y = -2(x+1)^2 - (x-3)^2 - 10 ] [ y = -2(x^2 + 2x + 1) - (x^2 - 6x + 9) - 10 ] [ y = -2x^2 - 4x - 2 - x^2 + 6x - 9 - 10 ] [ y = -3x^2 + 2x - 21 ]

Now, we have the equation in standard quadratic form: (y = ax^2 + bx + c) where (a = -3), (b = 2), and (c = -21). We can use the quadratic formula to find the roots:

[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}] [x = \frac{{-2 \pm \sqrt{{2^2 - 4(-3)(-21)}}}}{{2(-3)}}] [x = \frac{{-2 \pm \sqrt{{4 - 252}}}}{{-6}}] [x = \frac{{-2 \pm \sqrt{{-248}}}}{{-6}}] [x = \frac{{-2 \pm 2i\sqrt{62}}}{{-6}}] [x = \frac{{1 \pm i\sqrt{62}}}{{3}}]

So, the roots of the equation are:

[x = \frac{{1 + i\sqrt{62}}}{{3}}] (Imaginary) [x = \frac{{1 - i\sqrt{62}}}{{3}}] (Imaginary)

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7