If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of ‘k’ is
Answers
Step-by-step explanation:
Given :-
One zero of the quadratic polynomial
x²+3x+k is 2
To find :-
The value of k ?
Solution :-
Method-1:-
Given quadratic polynomial is x²+3x+k
Let P(x) = x²+3x+k
On comparing this with the standard quadratic polynomial ax²+bx+c then
a = 1
b = 3
c = k
One of the zeroes = 2
Let the another zero be A
We know that
Sum of the zeroes = -b/a
=> 2+A = -3/1
=> 2+A = -3
=> A = -3-2
=> A = -5 --------(1)
Therefore, Other zero = -5
We know that
Product of the zeroes = c/a
=> 2×A = k/1
=> 2×A = k
=> 2×-5 = k
=> -10 = k
Therefore, k = -10
Method -2:-
Given quadratic polynomial is x²+3x+k
Let P(x) = x²+3x+k
One of the zeroes = 2
We know that
If 2 is a zero then it satisfies the given polynomial P(x) i.e. P(2) = 0
=> P(2) = 2²+3(2)+k = 0
=> 4+6+k = 0
=> 10+k = 0
=> k = 0-10
=> k = -10
Therefore, k = -10
Answer :-
The value of k for the given problem is -10
Check:-
If k = -10 then the given polynomial will be x²+3x-10
=> x²+5x-2x-10
=> x(x+5)-2(x+5)
=> (x+5)(x-2)
To get zeroes of the polynomial P(x) then we write P(x) = 0
=> (x+5)(x-2) = 0
=> x+5 = 0 or x-2 = 0
=> x = -5 or x = 2
The zeroes are -5 and 2
One of the zeroes of P(x) is 2
Verified the given relations in the given problem.
Used formulae:-
→ The standard quadratic polynomial is ax²+bx+c
→ Sum of the zeroes = -b/a
→ Product of the zeroes = c/a
→ We can write P(x) = 0 to get the zeroes of P(x)
→ If a real number k is a zero of the polynomial P(x) then it satisfies the given polynomial i.e.P(k) = 0
K = -10
Step-by-step explanation:
Given :
P(x) = x² + 3x + k
One zero(α) = 2
To Find :
Value of k .
Solution :
As, Sum of zeros = α + β = -b/a
⇒ 2 + β = -3/1
⇒ β = -3 - 2 = -5
- Other zero (β) = -5
then, as Product of zeros = αβ = c/a
⇒ 2(-5) = k/1
⇒ -10 = k
FINAL ANSWER :
value of k is -10 .