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# Find the value of k so that each parabola has only one x - intercept of following question!?

c) 25x^2 + 20x + k

### 2 Answers

- 1 decade agoFavorite Answer
There's an equation in math called the discriminant that basically tells you how many x-intercepts (or roots) there are in a parabola. It is b^2-4ac. You might notice that it's a part of the quadratic equation. So, if b^2-4ac is greater than 0, the parabola has two or more roots. If it equals 0, then there is only one root. If it is less than 0, then there are no roots.

So what you need to do is since there is one root (x-intercept), you use the equation b^2-4ac=0. You plug in 20 for b, 25 for a, and k for c. You get: 625-80k=0. Then you can add 80k to both sides to get 80k=625. Divide both sides by 80 to get k, which is 7.8125.

Source(s): Brains are tasty. - hayharbrLv 71 decade ago
John had the right idea but if b = 20 then b^2 = 400 so you'd have 400 - 4(25)k = 0

400 - 100k = 0

400 = 100k

4 = k