Question

Find the missing term. The roots of x2 − ( ) + 34 are 5 ± 3i.

Answer 1

the required equation is:

`x^2 -10 +34`

Explanation:

The equation given is:

`x^2 -()+34`

Comparing it with standard quadratic equation

`a^2 +bx+c`

a= 1,

b=?

C= 34

We can find the value of b using Vieta's formulas :

That states that if roots x₁ and x₂ are given then,

x₁ + x₂ = -b/a

We are given roots: 5 ± 3i i.e, x₁= 5 + 3i and x₂= 5 - 3i

solving

5 + 3i + 5 - 3i = -b/1

10 = -b

Since the given equation already gives b as -b so, -b= 10 => b=10

Putting value of b in the missing place the required equation will be:

`x^2 -10 +34`