Question

Question 291 ptHow many real solutions does the quadratic equation below have?y = 2? + 5x + 100 1 real solutionNo real solutions2 real solutionsInfinite number of real solutionsNexDrevious

Answer 1

The quadratic equation is:

`y=2x^2+5x+10`

To find if the number of solutions, we use the discriminant of the equation. But first, we compare the given equation with the general quadratic equation:

`y=ax^2+bx+c`

By comparison, we find the values of a, b, and c:

`\begin{gathered} a=2 \\ b=5 \\ c=10 \end{gathered}`

Now, as we said previously, we have to use the discriminant to find the number of solutions. The discriminant is defined as follows:

`D=b^2-4ac`

• If the value of D results to be equal to 0, there will be 1 real solution.

• If the value of D results to be greater than 0, there will be 2 real solutions.

• And if the value of D results to be less than 0, there will be no real solutions.

We substitute a, b and c into the discriminant formula:

`D=5^2-4(2)(10)`

Solving the operations:

`\begin{gathered} D=25-4(2)(10) \\ D=25-80 \\ D=-55 \end{gathered}`

As we can see, the value of D is less than 0 (D<0) which indicates that there will be no real solutions for this quadratic equation.

Answer: No real solutions