Question

Find all values of for which the quadratic equation has two real solutions.5x^2+9x+h=0Write your answer as an equality or inequality in terms of .

Answer 1

Given the equation:

`5x^2+9x+h=0`

we will find the value of h which the quadratic equation has two real solutions

We will use the discriminant of the equation (D)

`\begin{gathered} a=5,b=9,c=h \\ D=b^2-4ac \end{gathered}`

substitute with the values of a, b, and c

`\begin{gathered} D=9^2-4\cdot5\cdot h \\ D=81-20h \end{gathered}`

the quadratic equation has two real solutions when D≥0

So,

`\begin{gathered} 81-20h\ge0 \\ -20h\ge-81\rightarrow(/-20) \\ (-20h)/(-20)\le(-81)/(-20) \\ \\ h\le4.05 \end{gathered}`

So, the answer will be:

`h\le4.05`