Question

State the sum of the roots of the quadratic equation. Then state the product of the roots of the quadratic equation. DO NOT SOLVE.A) 2x^2-5x +1 = 0B) x^2 + 8x - 3 = 0

Answer 1

A)

The sum of roots: 2.5

The product of the root: 0.5

B)

The sum of roots: -8

The product of the root: -3

Explanation:

The sum of the roots can be obtained using the following expression:

`x_1+x_2=-(b)/(a)`

We calculate in each case:

`\begin{gathered} 2x^2-5x+1=0\rightarrow a=2,b=-5 \\ \\ x_1+x_2=-(-5)/(2)=2.5 \\ \\ x^2+8x-3=0\rightarrow a=1,b=8 \\ \\ x_1+x_2=-(8)/(1)=-8 \end{gathered}`

Now, in the case of the product of roots, we calculate it by means of the following expression:

`x_1\cdot x_2=(c)/(a)`

We calculate in each case:

`\begin{gathered} 2x^2-5x+1=0\rightarrow a=2,c=1 \\ \\ x_1\cdot x_2=(1)/(2)=0.5 \\ \\ x^2+8x-3=0\rightarrow a=1,c=-3 \\ \\ x_1\cdot x_2=(-3)/(1)=-3 \end{gathered}`