Determine the exact value of \( k \) so that the quadratic function \( f(x) = x^2 - kx + 5 \) has only one zero.

I like this question. When we factorise this question the brackets have to be identical. 5 has to be square rooted to become √5. From, FOIL we know that the last digit is times by the other last digit to find the 5, as our brackets are identical this number is the same. The square root of 5. This number is doubled in identical brackets to find the middle number. so it is 2√5. As there is a minus number there the brackets are: (x-√5)(x-√5). Multiplying this out gives us: x²-2√5 x+5. k=2√5 (or -2√5, depending on if the minus is counted or not)

Answered by blatsoblatso | 2024-06-10

To find the value of k so that the quadratic function f(x) = x² - kx + 5 has only one zero, we need to ensure that the discriminant of the quadratic formula is equal to 0. In this case, the discriminant is 0 = (-k)² - 4(1)(5) = k² - 20. Setting this equal to 0, we have k² - 20 = 0, which gives k = ±√20, and since we want exactly one zero, k = √20.
Therefore, the exact values of k = ±√20, which are approximately 4.47 and -4.47.

Answered by qworange | 2024-06-24

The values of k that make the quadratic function f ( x ) = x 2 − k x + 5 have only one zero are k = 2 5 ​ and k = − 2 5 ​ . This is determined by setting the discriminant equal to zero. Hence, the quadratic has a double root at these values for k .
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Answered by blatsoblatso | 2024-12-26