Show that the polynomial f(x)=x to the power of 4 plus 4 x squared plus 6 has no zero.

Asked by araima2001 | 10th Jun, 2015, 12:59: PM

Expert Answer:

Subsitute x2=t in the polynomial to get
f(t)=t2+4t+6, a quadratic polynomial in 't'
Discriminant D of the above quadratic is 4- 4 X 1 X 6 = 16 - 24 = -8
Since, discriminant of the quadratic is negative, the quadratic has no real roots. 
Hence, for no real value of 't', the equation t2+4t+6=0 is satisfied. So, the equation has no zeroes. 

Answered by satyajit samal | 10th Jun, 2015, 03:50: PM