# for the function y=2x^2+5X-k one of the zeros is at x=-4. Determine the other x intercept.Full thorough explanation of solution and steps

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We have y= 2x^2 + 5x - k which is a quadratic equation and we are given that one of the roots is at x = -4.

The roots of 2x^2 + 5x - k lie at :

x = -5/4 + sqrt (25 + 8k)/4 and x = -5/4 - sqrt (25 + 8k)/4

As one of the roots is -4

-5/4 - sqrt (25 + 8k)/4 = -4

=> -5 - sqrt(25 + 8k) = -16

=> sqrt(25 + 8k) = 11

=> (25 + 8k) = 121

=> (25 + 8k) = 121

=> 8k = 96

=> k = 12

The other root is at x = -5/4 + sqrt (25 + 8k)/4

=> x = -5/4 + sqrt (25 + 96)/4

=> -5/4 + 11/4

=> 6/4

=> 3/2

As x = 3/2 is the other root, this is also the point where the other x-intercept lies.

**The other x-intercept of y = 2x^2 + 5x - k is (3/2, 0).**

y= 2x^2 + 5x - k

Given that x= -4 is one of the zeros.

Then we know that y(-4) = 0

We will substitute to find K.

==> 0 = 2(-4)^2 + 5(-4) - k

==> 0 = 32 - 20 -k

==> 0 = 12-k

==> k= 12

==> y= 2x^2 + 5x - 12

Now we know that x= -4 is one of the roots, then x+ 4 is a factor.

==> y= (x+4)(2x -3)

==> Then the other root ( x-intercept) is when 2x-3 = 0 ==> x = 3/2

**Then the other x-intercept is 3/2**

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