if the sum of the zeros of the quadratic polynomial P of x is equal to K square + 2 X + 3 K is equal to the product of its zeros then the value of k is
Answers
Correct Question:
If the sum of the zeros of the quadratic polynomial p(x) = kx² + 2x + 3k is equal to the product of it's zeros , then find the value of k .
Answer:
k = -2/3
Note:
∆ The general form of a quadratic polynomial is given as ; p(x) = ax² + bx + c .
∆ If A and B are the zeros of the quadratic polynomial p(x) = ax² + bx + c , then ;
• Sum of zeros,(A+B) = - b/a
• Product of zeros,(A•B) = c/a
∆ If A and B are given zeros of a quadratic polynomial p(x)., then p(x) will be given as ;
p(x) = x² - (A+B)x + A•B .
Solution:
The given polynomial is ;
p(x) = kx² + 2x + 3k
Clearly, here we have ;
a = k
b = 2
c = 3k
Also,
Let A and B be the zeros of the given polynomial p(x) , then ;
• Sum of the zeros will be ;
=> A + B = -b/a
=> A + B = -2/k ------------(1)
• Product of the zeros will be ;
=> A•B = c/a
=> A•B = 3k/k
=> A•B = 3 -----------(2)
Also,
It is given that , the sum and the product of the zeros of given quadratic polynomial are equal.
Thus,
A + B = A•B -------------(3)
Now,
From eq-(1) and eq-(3) , we have ;
A•B = -2/k ----------(4)
Again,
From eq-(2) and eq-(4) , we have ;
=> 3 = -2/k
=> k = -2/3
Hence,
The required value of k is (-2/3) .
# Probable Question:
If the sum of the zeros of the quadratic polynomial p(x) = x² + 2x + 3k is equal to the product of it's zeros , then find the value of k .
Answer:
k = -2/3
Solution:
The given polynomial is ;
p(x) = x² + 2x + 3k
Clearly, here we have ;
a = 1
b = 2
c = 3k
Also,
Let A and B be the zeros of the given polynomial p(x) , then ;
• Sum of the zeros will be ;
=> A + B = -b/a
=> A + B = -2/1
=> A + B = -2 ------------(1)
• Product of the zeros will be ;
=> A•B = c/a
=> A•B = 3k/1
=> A•B = 3k -----------(2)
Also,
It is given that , the sum and the product of the zeros of given quadratic polynomial are equal.
Thus,
A + B = A•B -------------(3)
Now,
From eq-(1) and eq-(3) , we have ;
A•B = -2 ----------(4)
Again,
From eq-(2) and eq-(4) , we have ;
=> 3k = -2
=> k = -2/3
Hence,
The required value of k is (-2/3) .
Answer:
The above answer is correct ✔
Step-by-step explanation:
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