Question

If one root of quadratic equation x²+kx-8=0 is -4 then the value of k

Answer 1

Answer:

x = -4

x²+kx-8=0

(-4)² + k(-4) - 8 = 0

16 -4k -8 = 0

-4k + 8 = 0

4k = 8

k = 2

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Answer 2

SOLUTION

GIVEN

One root of quadratic equation x² + kx - 8 = 0 is - 4

TO DETERMINE

The value of k

EVALUATION

Here the given equation is

x² + kx - 8 = 0

Now - 4 is one of the zeros of the quadratic equation

Thus we get

$\displaystyle \sf{ {( - 4)}^{2} + k \times ( - 4) - 8 = 0}$

$\displaystyle \sf{ \implies 16 - 4k - 8 = 0}$

$\displaystyle \sf{ \implies 8 - 4k = 0}$

$\displaystyle \sf{ \implies - 4k = - 8}$

$\displaystyle \sf{ \implies k = 2}$

FINAL ANSWER

Hence the required value of k = 2

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