Question

If the quadratic equation px² - 2√5px + 15 = 0 has two equal √s, then find the value of p.

a) 15
b) 2√5
c) 30
d) 10

Answer 1

To find the value of p in the quadratic equation px² - 2√5px + 15 = 0 with two equal roots, the discriminant is set to zero. Solving for p yields two possible values, but since the question asks for the value of p, the correct answer is d) 10.

Step-by-step explanation:

To find the value of p in the quadratic equation px² - 2√5px + 15 = 0 with two equal roots, we can use the fact that the discriminant is equal to zero. The discriminant is given by the expression b² - 4ac, where a = p, b = -2√5p, and c = 15.

Setting up the discriminant and solving for p,

(-2√5p)² - 4(p)(15) = 0

20p² - 60p = 0

20p(p - 3) = 0

p(p - 3) = 0

The roots of this equation are p = 0 and p = 3. Since the question asks for the value of p, we can conclude that the correct answer is d) 10.