Question

Please solve all question given in photo

Answer 1

Hello friend
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3) (i) If x = -1/3 is a zero of polynomial p(x) = 3x + 1 then p(-1/3) should be 0.
At, p(-1/3) = 3(-1/3) + 1 = -1 + 1 = 0
Therefore, x = -1/3 is a zero of polynomial p(x) = 3x + 1.


(ii) If x = 4/5 is a zero of polynomial p(x) = 5x - π then p(4/5) should be 0.
At, p(4/5) = 5(4/5) - π = 4 - π
Therefore, x = 4/5 is not a zero of given polynomial p(x) = 5x - π.


(iii) If x = 1 and x = -1 are zeroes 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 zeroes of the polynomial  p(x) = x² - 1.


(iv) If x = -1 and x = 2 are zeroes of polynomial p(x) = (x +1) (x - 2), then p( - 1) and (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
Therefore, x = -1 and x = 2 are zeroes of the 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 a zero of the polynomial p(x) = x².


(vi) if x =  -m/l is a zero of polynomial p(x) = lx + m , then p(-m/l) should be 0.
Here , p(-m/l) = l(-m/l) + m = -m + m = 0
Therefore, x = -m/l is a zero of the given polynomial.


(vii) if x = -1/√3 and x = 2/√3 are zeroes of polynomial p(x) = 3x² - 1 , then
p(-1/√3) and p(2/√3) should be 0
Here, p(-1/√3) = 3(-1/√3)² - 1 = 3(1/3) - 1 = 1-1 = 0 , and
p(2/√3) = 3(2/√3)² - 1 = 3(4/3) - 1 = 4 - 1 = 3
Hence, x = -1/√3 is a zero of the given polynomial. x = 2/√3 is not a zero of the given polynomial.


(viii)  If x = 1/2 is a zero of polynomial p(x) = 2x + 1 then p(1/2) should be 0.
At, p(1/2) = 2(1/2) + 1 = 1 + 1 = 2
Therefore, x = 1/2 is not a zero of given polynomial p(x) = 2x + 1.


4) (i) p(x) = x + 5 p(x) = 0x + 5 = 0x = -5Therefore, x = -5 is a zero of polynomial p(x) = x + 5 .

(ii) p(x) = x - 5p(x) = 0x - 5 = 0x = 5Therefore, x = 5 is a zero of polynomial p(x) = x - 5.


(iii) p(x) = 2x + 5 
p(x) = 0
2x + 5 = 0
2x = -5
x = -5/2
x = -5/2 is a zero of the given polynomial


(iv) p(x) = 3x - 2
p(x) = 0
3x - 2 = 0
x = 2/3
x = 2/3 is a zero of the given polynomial


(v) p(x) = 3x
p(x) = 0
3x = 0
x = 0
x = 0 is a zero of the given polynomial 


(vi) p(x) = ax
p(x) = 0
ax = 0
x = 0
x = 0 is a zero of the given polynomial


(vii) p(x) = cx + d
p(x) = 0
cx + d = 0
x = -d/c
x = -d/c is a zero of the given polynomial
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Hope it will help you

thanks,

Swapnil756   Core

Answer 2

hey there,

1.  x = -1/3 is a zero of polynomial p(x) = 3x + 1.
2. x = 4/5 is not a zero of given polynomial p(x) = 5x - π.
3. x = 1 and -1 are zeroes of the polynomial  p(x) = x² - 1.
4. x = -1 and x = 2 are zeroes of the polynomial p(x) = (x +1) (x - 2).
5.  x = 0 is a zero of the polynomial p(x) = x².
6.  x = -m/l is a zero of the given polynomial.
7. , x = -1/√3 is a zero of the given polynomial. x = 2/√3 is not a zero of the given polynomial.
8.  x = 1/2 is not a zero of given polynomial p(x) = 2x + 1.
9. x = -5 is a zero of polynomial p(x) = x + 5 .
10.  x = 5 is a zero of polynomial p(x) = x - 5.
11. x = -5/2 is a zero of the given polynomial
12. x = 2/3 is a zero of the given polynomial
13. x = 0 is a zero of the given polynomial 
14. x = 0 is a zero of the given polynomial
15. x = -d/c is a zero of the given polynomial

Hope this helps!