Find the zeroes of the given polynomials
(i) p(x) = 3x
(ii) p(x) = x² + 5x + 6
Answers
✰ Qᴜēsᴛíõñ :-
Find the zeroes of the given polynomials
(i) p(x) = 3x
(ii) p(x) = x² + 5x + 6
✪ Söʟúᴛîøɴ :-
(i) Given p(x) = 3x
Let p(x) = 0
So, 3x = 0
x = 0/3 = 0
Zeroes of the p(x) = 3x is one
⛬ Number of zeroes is one
(ii) Given p(x) = x² + 5x + 6 is a quadratic polynomial.
It has almost 2 zeroes
To find zeroes, let p(x) = 0
➙ x² + 5x + 6 = 0
➙ x² + 3x + 2x + 6 = 0
➙ x(x + 3) + 2 (x + 3) = 0
➙ (x + 3) (x + 2) = 0
➙ x + 3 = 0 or x + 2 = 0
➙ x = -3 or x = -2
⛬ The zeroes of the polynomial are -3 and -2
Answer:
(i) p(x) = 3x
Ans: 0
(ii) p(x) = x² + 5x + 6
Ans: (-3) and (-2)
Step-by-step explanation:
Method of finding zeroes
(i) Method for first question :
First of all we have to write the value of the p(x) in the left hand side (LHS) which is given in the question. Then we have to write the number "0" in the right hand side of the equation (RHS). After that we have to equate both the sides. After that we have to find the value of x in the given equation.
(i) p(x) = 3x
=> 3x = 0
=> x = 0/3
=> x = 0
So, the zeroes of the polynomial equation p(x) = 3x is 0.
(ii) Method for the second question :
First of all we have to write the value of the p(x) in the left hand side (LHS) which is given in the question. Then we have to write the number "0" in the right hand side of the equation (RHS). After that we have to factories the equation because it is a quadratic equation on both the sides. After that we have to find the value of x in the two finded equation from the factorization method.
(ii) p(x) = x² + 5x + 6
=> x² + 5x + 6 = 0
=> x ( x + 3 ) + 2 ( x + 2 ) = 0
=> ( x + 3 ) ( x + 2 ) = 0
=> x + 3 = 0 "or" x + 2 = 0
=> x = -3 "or" x = -2
So, the zeroes of the polynomial equation p(x) = x² + 5x + 6 is (-3) and (-2) respectively.
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