Question 3. Verify whether the following are zeroes of the polynomial, indicated against Chapter 2: Polynomial Maths Class 9 solutions are developed for assisting understudies with working on their score and increase knowledge of the subjects. Question 3. Verify whether the following are zeroes of the polynomial, indicated against them. (i) p(x) = 3x + 1, x = - 1/3 (ii) p(x) = 5x – π, x = 4/5 (iii) p(x) = x2 – 1, x = 1, –1 (iv) p(x) = (x + 1) (x – 2), x = – 1, 2 (v) p(x) = x2, x = 0 (vi) p(x) = lx + m, x = –m/l (vii) p(x) = 3x2 – 1, x = - 1/√3 , 2/√3 (viii) p(x) = 2x + 1, x =1/2 is solved by our expert teachers. You can get ncert solutions and notes for class 9 chapter 2 absolutely free. NCERT Solutions for class 9 Maths Chapter 2: Polynomial is very essencial for getting good marks in CBSE Board examinations
Question 3. Verify whether the following are zeroes of the polynomial, indicated against them.
(i) p(x) = 3x + 1, x = - 1/3
(ii) p(x) = 5x – π, x = 4/5
(iii) p(x) = x2 – 1, x = 1, –1
(iv) p(x) = (x + 1) (x – 2), x = – 1, 2
(v) p(x) = x2, x = 0
(vi) p(x) = lx + m, x = –m/l
(vii) p(x) = 3x2 – 1, x = - 1/√3 , 2/√3
(viii) p(x) = 2x + 1, x =1/2
Solution: (i) p(x) = 3x + 1, x = - 1/3
Plug x = -1/3
=> p(x) = 3x + 1
=>p(-1/3) = 3(-1/3) +1
=>p(-1/3) = -1 +1
=>p(-1/3) = 0
When P(a) = 0 then a is always zero of polynomial
Hence -1/3 is zero of polynomial p(x) = 3x + 1
(ii) p(x) = 5x – π, x = 4/5
Plug x = 4/5 we get
=> p(4/5) = 5x – π,
=> p(4/5) = 5(4/5) – π,
=> p(4/5) = 4 – π,
And pi = 22/7 so that
=> p(4/5) = 4 – 22/7 is not = 0
Hence 4/5 is not zero of polynomial p(x) = 5x – π
(iii) p(x) = x2 – 1, x = 1, –1
Plug x = - 1
=> p(x) = x2 – 1
=> p(-1) = (-1)2 – 1
=> p(-1) = 1 – 1
=> p(-1) = 0
Plug x = 1
=> p(x) = x2 – 1
=> p(1) = (1)2 – 1
=> p(1) = 1 – 1
=> p(1) = 0
Hence both x = - 1 and 1 are zero of polynomial p(x) = x2 – 1
(iv) p(x) = (x + 1) (x – 2), x = – 1, 2
Plug x = - 1
=>p(x) = (x + 1) (x – 2)
=>p(-1) = (-1 + 1) (-1 – 2)
=>p(-1) = (0) (-3)
=>p(-1) = 0
Now plug x = 2 we get
Plug x = 2
=>p(x) = (x + 1) (x – 2)
=>p(2) = (2 + 1) (2 – 2)
=>p(2) = (3) (0)
=>p(2) = 0
Hence -1 and 2 both are zero of the polynomial p(x) = (x + 1) (x – 2)
(v) p(x) = x2, x = 0
Plug x = 0 we get
=>p(x) = x2
=>p(0) = (0)2
=>p(0) = 0
Hence 0 is the zero so polynomial p(x) = x2
(vi) p(x) = lx + m, x = –m/l
Plug x = - m/l we get
=> p(x) = lx + m
=> p(-m/l) = l(-m/l) + m
=> p(-m/l) = -m + m
=> p(-m/l) = 0
Hence - m/l is the zero of polynomial p(x) = lx + m
(vii) p(x) = 3x2 – 1, x = - 1/√3 , 2/√3
Plug x = - 1/ √3 we get
=>p(x) = 3x2 – 1
=>p(-1/√3) = 3(-1/√3)2 – 1
=>p(-1/√3) = 3(1/3) – 1
=>p(-1/√3) = 1 – 1
=>p(-1/√3) = 0
Plug x = 2/ √3 we get
=>p(x) = 3x2 – 1
=>p(1/√3) = 3(2/√3)2 – 1
=>p(1/√3) = 3(4/3) – 1
=>p(1/√3) = 4 – 1
=>p(1/√3) = 3
Hence x = - 1/√3 is zero of the polynomial p(x) = 3x2 – 1
But x = 2/√3 is not a zero of the polynomial
(viii) p(x) = 2x + 1, x =1/2
Plug x = ½ we get
=> p(x) = 2x + 1
=> p(1/2) = 2(1/2) + 1
=> p(1/2) = 2(1/2) + 1
=> p(1/2) = 1 + 1
=> p(1/2) = 2
Hence ½ is not a zero of polynomial p(x) = 2x + 1
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