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CBSE Class 10 Answered

<div>Show that the polynomial f(x)=<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=87629605ccb81f5590f02981e094ef96.png" alt="x to the power of 4 plus 4 x squared plus 6" align="middle" />&nbsp;has no zero.</div>
Asked by araima2001 | 10 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 | 10 Jun, 2015, 03:50: PM
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