Question

Use the discriminant to determine the number of real solutions for each quadratic equation. Do not solve.A) x^2+7x+10=0B) 4x^2-3x+4=0

Answer 1

(a)Two real solutions.

(b)No real solution

Step-by-step explanation:

The discriminant of a standard quadratic function y=ax²+bx+c is obtained by using the formula:

`D=b^2-4ac`

Part A

`\begin{gathered} x^2+7x+10=0 \\ a=1,b=7,c=10 \end{gathered}`

Therefore:

`\begin{gathered} D=7^2-4(1)(10) \\ =49-40 \\ =9 \\ D>0 \end{gathered}`

Since D is greater than 0, the quadratic equation has two distinct real solutions.

Part B

`\begin{gathered} 4x^2-3x+4=0 \\ a=4,b=-3,c=4 \end{gathered}`

Therefore:

`\begin{gathered} D=(-3)^2-4(4*4) \\ =9-64 \\ =-55 \\ D<0 \end{gathered}`

Since D is less than 0, the quadratic equation has No real solution.