Respuesta :

Since its roots are -4 and 2 and a = 1 [The coefficient of x^2] we know that x^2 + bx + c = (x - (-4)) (x-2)=(x+4)(x-2) = 0. Using the distributive property we get, x^2 + 2x - 8 = 0. By equating coefficients (common strategy for partial fractions and undetermined coefficient method of solving ODE), we get b = 2 and c = -8.

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The values of b and c are b = 2 and c =−8

From the question, we are given the roots of the quadratic equation as −4 and 2.

To find b and c, we will first determine the quadratic equation.

  • To determine the equation,

Since the roots are −4 and 2

Then we can say that

x = −4 or x =2

Then we can write that

x + 4 = 0 or x − 2 = 0

Then, we can write the two equations as

(x + 4)(x − 2) = 0

Now, we will open the brackets

We can write that

x(x − 2) +4 (x − 2) = 0

Then,

x² −2x +4x −8 = 0

Simplifying further

x² +2x −8 = 0

∴ The quadratic equation is x² +2x −8 = 0

Now, to determine the values of b and c, we will compare the quadratic equation to the given form x² +bx +c = 0

By comparison, b = 2 and c =−8

Hence, the values of b and c are b = 2 and c =−8

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