Question

1. If the sum of zereos of the quadratic
polynomial f(t) = k t² +2t +3k is equal to
their product find the value of k​

Answer 1

Given:-

→ Polynomial : f(t) = kt² + 2t + 3k

→ Sum of zeros = Product of zeros

To find:-

→ Value of p?

Solution:-

Here,

• a = k
• b = 2
• c = 3k

We know,

→ Sum of zeros = -b/a

→ Sum of zeros = -2/k

Now we also know,

→ Product of zeros = c/a

→ Product of zeros = 3k/k

→ Product of zeros = 3

A/q,

→ -2/k = 3

→ 3k = -2

→ k = -2/3

Therefore,

Required value of k = (-2/3)

Answer 2

Step-by-step explanation:

Given -

sum of zeroes = product of zeroes

• α + β = αβ
• polynomial f(t) = kt² + 2t + 3k

To Find -

Value of k

As we know that :-

sum of zeroes = α + β = -b/a

and

product of zeroes = αβ = c/a

According to the question :-

sum of zeroes = product of zeroes

It means,

• α + β = αβ Or -b/a = c/a

In polynomial f(t) = kt² + 2t + 3k

here,

a = k

b = 2

c = 3k

Now,

-2/k = 3k/k

» -2/k = 3

» k = -2/3

Hence,

The value of k is -2/3