Question

Which equation has no real solutions?(А)2x2+2x+15= 02x2 + 5x - 3=0© x2 + 7x+2=0x2 - 4x + 2 = 0

Answer 1

We are asked to find out which of the given quadratic equation has no real solutions.

Recall that a quadratic equation has no real solutions if the discriminant is less than 0.

The discriminant is given by

`d=b^2-4ac`

Where a, b, and c are the coefficients of the quadratic equation.

Let us analyze each of the given quadratic equations.

Option A:

`2x^2+2x+15=0`

The coefficients are

a = 2

b = 2

c = 15

The discriminant is

`\begin{gathered} d=b^2-4ac \\ d=2^2-4(2)(15) \\ d=4-120 \\ d=-116 \end{gathered}`

As you can see, the discriminant is less than 0, therefore, this quadratic equation has no real solutions.

Therefore, the correct answer is option A.