Question

If 1 is root of the quadratic equation 3x^2+ax-2=0 and the quadratic equation a(x2+6x)-b=0has equal roots find the value of b

Answer 1

ax2-3x+1=0

One root of this equation is (2+i)

So put x=(2+i)

a(2+i)2–3(2+i)+1=0

a(4+2i)-6-3i+1=0

a(4+2i)-5-3i=0

a=5+3i/4+2i

Rationalise the denominator

a=(5+3i)(4–2i)/(4+2i)(4–2i)

a=20–10i+12i+6/16+4

a=26–2i/20

So the value of a is 13-i/10