Question

Use the discriminant to determine the number of real solutions to the quadratic equation.

70w2 - 12w + 1 = 0
What is the number of real solutions?

Answer 1

There are two real and different roots

Explanation:

The discriminant is given by b²-4ac

(-12)²-4(70×1)

144-280

136

Now 136>0

Answer 2

Let D = discrimination

Rules:

If D > 0, there are 2 real number solutions.

If D = 0, there is only 1 real number solution.

If D < 0, there are 2 imaginary solution.

Given 70w2 - 12w + 1 = 0, b = -12, a = 70 and c = 1.

D = b^2 - 4ac

D = (-12)^2 - 4(70)(1)

D = 144 - 280

D = -136

Our D value is less than 0.

Our case is D < 0.

This means the given quadratic equation has 2 imaginary solutions.