# Verify whether th

For any value of x, say a, to be a zero of polynomial p(a) = 0

Keeping that in mind,

(i) Here p(x)= 3x + 1 ,  for x = -1/3 Therefore, x = –1/3 is a zero of polynomial p(x) = 3x + 1

(ii) here p(x) = 5x - π, for x = 4/5, Since, Therefore, x = 4/5  is not a zero of polynomial p(x) = 5x - π

(iii) If x = 1 and x = -1 are zeros of polynomial p(x) = x2 - 1 then p (1) and p (-1) should be 0

At, p (1) = (1)2 – 1 = 0 and,

At, p (-1) = (-1)2 – 1 = 0

Hence, x = 1 and -1 are zeros of polynomial p (x) = x2 - 1

(iv) If x = -1 and x = 2 are zeros of polynomial p(x) = (x + 1) (x – 2) then p (-1) and p (2) should be 0

At, p (-1) = (-1 + 1) (- 1 – 2) = 0 (-3) = 0 and,

At, p (2) = (2 + 1) (2 – 2) = 3 (0) = 0

Hence, x = -1 and x = 2 are zeros of polynomial p (x) = (x + 1) (x – 2)

(v) If x = 0 is a zero of polynomial p (x) = x2

Then, p (0) should be zero

Here, p (0) = (0)2 = 0

Hence, x = 0 is the zero of the polynomial p (x) = x2

(vi) If x = is a zero of the polynomial p(x) = lx + m then p ( ) should be 0 Therefore, x = is the zero of the polynomial p(x) = l x + m

(vii) If x = and x = are zeros of the polynomial p(x) = 3 x2 – 1, then

p( ) and p( ) should be 0

At, p ( ) = 3 ( )2 – 1

= 3 ( ) – 1

= 1 – 1 = 0 and,

At, p ( ) = 3 ( )2 – 1

= 3 ( ) – 1

= 4 – 1 = 3

Therefore, x = is a zero of the polynomial p(x) = 3x2 + 1

But, x = is not a zero of the polynomial

(viii) If x = is a zero of polynomial p (x) = 2x + 1 then p(1/2) should be zero

At, p ( ) = 2 ( ) + 1

= 1 + 1 = 2

Therefore, x = is not a zero of given polynomial p(x) = 2x + 1

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

The zeroes of theRS Aggarwal & V Aggarwal - Mathematics

Zero of the polynRS Aggarwal & V Aggarwal - Mathematics

If 2 and -1/3 areRS Aggarwal & V Aggarwal - Mathematics

If (x + 1) is a fRS Aggarwal & V Aggarwal - Mathematics

If (x2RS Aggarwal & V Aggarwal - Mathematics

The zeroes of theRS Aggarwal & V Aggarwal - Mathematics

The zeroes of theRS Aggarwal & V Aggarwal - Mathematics

If p(x) = x3RS Aggarwal & V Aggarwal - Mathematics

If p(x) = (xRS Aggarwal & V Aggarwal - Mathematics

The coefficient oRS Aggarwal & V Aggarwal - Mathematics