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For which of the following values of c will there be 2 distinct real solutions to the equation 5x2 + 16x + c = 0?
  • a)
    3
  • b)
    12
  • c)
    14
  • d)
    15
  • e)
    20
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
For which of the following values of c will there be 2 distinct real s...
Solution:

To find the values of c for which the quadratic equation 5x^2 + 16x + c = 0 has 2 distinct real solutions, we can use the discriminant formula. The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac.

If the discriminant is positive (D > 0), then the quadratic equation has 2 distinct real solutions. If the discriminant is zero (D = 0), then the equation has 2 identical real solutions. And if the discriminant is negative (D < 0),="" then="" the="" equation="" has="" no="" real="" />

In this case, we have the quadratic equation 5x^2 + 16x + c = 0. Comparing this with the general form ax^2 + bx + c = 0, we can see that a = 5, b = 16, and c = c.

Now, we can calculate the discriminant D using the formula D = b^2 - 4ac. Substituting the values, we get:

D = 16^2 - 4(5)(c)
D = 256 - 20c
D = 20(16 - c)

Since we want the equation to have 2 distinct real solutions, the discriminant D must be greater than zero:

D > 0
20(16 - c) > 0
16 - c > 0
c < />

Therefore, the values of c for which the equation has 2 distinct real solutions are all values less than 16. Among the given options, the only value less than 16 is 3. Hence, the correct answer is option A: 3.
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Community Answer
For which of the following values of c will there be 2 distinct real s...
The best way to solve this problem is to plug in the answer choices for c, and factor the equation, starting with answer choice F: 5x2 + 16x + 3 = 0
(5x + 1)(x + 3) = 0
5x + 1 = 0, x = -1/5
x + 3 = 0; x = −3
Answer choice A gives you 2 distinct solutions for x, so you do not need to try the remaining answer choices. Using the quadratic formula to solve the other choices will not give you real solutions.
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For which of the following values of c will there be 2 distinct real solutions to the equation 5x2 + 16x + c = 0?a)3b)12c)14d)15e)20Correct answer is option 'A'. Can you explain this answer?
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