Question

If (a-b) and (a+b) are zeroes of the polynomial f(x)=2x^3-6x^2+5x-7 find the value of a​

Answer 1

Answer:

Sorry, I rushed into this and my original answer was wrong.

Now I suspect there might be a mistake in the question itself, but nonetheless, I'll answer it as it is as best I can.

a = 2.5576    or    a = 0.2212

Step-by-step explanation:

The given cubic only has one real root and neither it nor the complex roots are simply expressible.  So resorting to a computer to factorize it, the cubic becomes

2(x - 2.5576)(x - (0.2212 + 1.1487i))(x - (0.2212 - 1.1487i))

So if a and b are meant to be real, then necessarily b=0 and a = 2.5576.

Otherwise, if we take a to be real and b to be pure imaginary, then a+b and a-b are the conjugate complex roots, with a = 0.2212.