Question

The quadratic equation with real Coefficient whose one root is 7 + 5i

Answer 1

Hey There!!


For any quadratic equation, if one root is complex, then the other root must be its complex conjugate.

Complex roots always occur in pairs for a quadratic equation.

So, if one root is 7+5i, then the other root is 7-5i

Now, we can easily find the quadratic equation.

Sum of roots = 7 + 5i + 7 - 5i = 14

Product of roots = (7+5i)(7-5i) = 49 + 25 = 74


For a quadratic equation $ax^2+bx+c=0$

Sum of roots = $\frac{-b}{a}$

Product of roots = $\frac{c}{a}$


So, here also we can write the quadratic equation as follows:



$\boxed{x^2-14x+74=0}$



Hope it helps
Purva
Brainly Community

Answer 2

answers given in attachment below