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Answer 1

Solution :

The given polynomial is

f(t) = kt² + 2t + 3k

If p and q are the zeroes of f(x), by the relation between zeroes and coefficients, we get

• p + q = - 2/k
• pq = 3k/k = 3

By the given condition, the sum of the zeroes = product of the zeroes

⇒ p + q = pq

⇒ - 2/k = 3

⇒ k = - 2/3

Answer 2

Answer:

Given polynomial in terms of t is

f (t) = kt^2 + 2t + 3k

given sum of the roots is equal to the product of the roots.

let the roots be (alpha) and (beta)

⭐ alpha + beta = alpha × beta

we know that

alpha + beta = - b /a

alpha × beta = c /a

» According to the question

- b / a = c /a

Here a = k , b = 2 ,c = 3k

- 2/k = 3k /k

-2 /k = 3

k = -2 /3

c = 3 k

c = 3 × -2/3

c = -2

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Polynomial :-

-2/3 t^2 +2t - 2

let's verify

alpha + beta = -b/a = -2/-2 /3= 3

alpha × beta = c /a = -2/-2 /3= 3

•°• alpha + beta = alpha × beta

Hence verified

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