Question

if the sum of the zeros of the polynomial P( x) = 3 k square + (2 k + 1) x - K + 5 is equal to the product of the zeros then find the value of k​

Answer 1

Answer:

see the attachment for answer

Step-by-step explanation:

your final answer is

K= -6.

I hope you get your answer

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Answer 2

Correct Question :- if the sum of the zeros of the polynomial P(x) = 3k x²+ (2 k + 1) x - K + 5 is equal to the product of the zeros then find the value of k ?

Concept used :-

The sum of the roots of the Equation ax² + bx + c = 0 , is given by = (-b/a)

and ,

→ Product of roots of the Equation is given by = c/a.

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Solution :-

Comparing The given Polynomial 3k x²+ (2 k + 1) x - K + 5 with ax² + bx + c , we get,

→ a = 3k

→ b = (2k + 1)

→ c = -k + 5

So,

→ sum of Roots of the given Equation = (-b/a) = -(2k+1)/3k

And,

→ Product of Roots of the given Equation = c/a = -k+5 / 3k

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Now, we have given That, sum of Roots is Equal to Product of Roots.

So,

⟿ - (2k + 1) / 3k = -k + 5 / 3k

Cancel 3k from Both Denominator ,

⟿ - 2k - 1 = - k + 5

⟿ - k + 2k = - 1 - 5

⟿ k = (-6) (Ans.)