Question

4
select the correct answer from each drop - down menu.
determine the number of real solutions for each of the given equations.

equation	number of solutions
$y = 2x^2 - 6x + 5$
$y = x^2 + 7x - 11$
$y = - x^2 - 8x - 16$

Explanation:

Step1: Calculate discriminant for \(y=-3x^2+x+12\)

Discriminant \(D = 1^2 - 4(-3)(12) = 1 + 144 = 145 > 0\), so 2 real solutions.

Step2: Calculate discriminant for \(y=2x^2-6x+5\)

Discriminant \(D = (-6)^2 - 4(2)(5) = 36 - 40 = -4 < 0\), so 0 real solutions.

Step3: Calculate discriminant for \(y=x^2+7x-11\)

Discriminant \(D = 7^2 - 4(1)(-11) = 49 + 44 = 93 > 0\), so 2 real solutions.

Step4: Calculate discriminant for \(y=-x^2-8x-16\)

Discriminant \(D = (-8)^2 - 4(-1)(-16) = 64 - 64 = 0\), so 1 real solution.

Answer:

2, 0, 2, 1