Question

find a quadratic polynomial whose zeroes are -1, 4/3​

Answer 1

Answer:

a quadratic polynomial whose zeroes are -1, 4/3 is 3x^2+3x-4.

Answer 2

Concept:

A quadratic polynomial is a polynomial that has the highest degree of two.

Given:

We have,

Zeroes of the quadratic polynomial are -1, 4/3​.

Find:

We are asked to find a quadratic polynomial.

Solution:

We have

Zeroes of the quadratic polynomial are -1, 4/3​.

So,

Let,

α = -1

And,

β = 4/3

So,

Sum of zeros = α + β = -1 + 4/3 = 1/3

And,

Product of zeros = α × β = (-1) × 4/3 = (-4/3)

Now,

We know that,

A quadratic polynomial is given by,

x² - (Sum of zeros)x + Product of zeros,

So,

Now,

Putting values,

We get,

x² - (1/3)x + (-4/3)

On solving we get,

3x² - x - 4

Hence, the quadratic polynomial whose zeroes are -1, 4/3​ is 3x² - x - 4.

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