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

Respuesta :

ANSWER:

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

STEP-BY-STEP EXPLANATION:

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

[tex]x_1+x_2=-\frac{b}{a}[/tex]

We calculate in each case:

[tex]\begin{gathered} 2x^2-5x+1=0\rightarrow a=2,b=-5 \\ \\ x_1+x_2=-\frac{-5}{2}=2.5 \\ \\ x^2+8x-3=0\rightarrow a=1,b=8 \\ \\ x_1+x_2=-\frac{8}{1}=-8 \end{gathered}[/tex]

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

[tex]x_1\cdot x_2=\frac{c}{a}[/tex]

We calculate in each case:

[tex]\begin{gathered} 2x^2-5x+1=0\rightarrow a=2,c=1 \\ \\ x_1\cdot x_2=\frac{1}{2}=0.5 \\ \\ x^2+8x-3=0\rightarrow a=1,c=-3 \\ \\ x_1\cdot x_2=\frac{-3}{1}=-3 \end{gathered}[/tex]