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x(kx−56)=−16 the given equation, k is an integer constant. if the equation has no real solution, what is the least possible value of k ?

User Lenz
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Final answer:

To find the least possible value of k for which the given equation has no real solution, we rearrange the equation to form a quadratic equation and solve for k using the discriminant formula. The least possible value of k is 50.

Step-by-step explanation:

To find the least possible value of k for which the given equation x(kx-56) = -16 has no real solution, we can start by rearranging the equation to form a quadratic equation:

x^2k-56x+16=0

We know that for a quadratic equation to have no real solutions, the discriminant (∆) must be negative. The discriminant is given by the formula ∆ = b^2 - 4ac.

In this case, a = k, b = -56, and c = 16. We now set ∆ to be less than 0 and solve for k:

(-56)^2 - 4(k)(16) < 0

3136 - 64k < 0

-64k < -3136

k > 49

Therefore, the least possible value of k for which the equation has no real solution is k = 50.

User Ptomli
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