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# Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, - 7, - 14 respectively.

**Solution:**

We know that the general form of a cubic polynomial is ax^{3} + bx^{2} + cx + d and the zeroes are α, β, and γ.

Let's look at the relation between sum, and product of its zeroes and coefficients of the polynomial.

- α + β + γ = - b / a
- αβ + βγ + γα = c / a
- α x β x γ = - d / a

Let the polynomial be ax^{3} + bx^{2} + cx + d and the zeroes are α, β, γ

We know that,

α + β + γ = 2/1 = - b / a

αβ + βγ + γα = - 7/1 = c / a

α.β.γ = - 14/1 = - d / a

Thus, by comparing the coefficients we get, a = 1, then b = - 2, c = - 7 and d = 14

Now, substitute the values of a, b, c, and d in the cubic polynomial ax^{3} + bx^{2} + cx + d.

Hence the polynomial is x^{3} - 2x^{2} - 7x + 14.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 2

**Video Solution:**

## Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, - 7, - 14 respectively

NCERT Solutions Class 10 Maths Chapter 2 Exercise 2.4 Question 2

**Summary:**

A cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, - 7, - 14 respectively is x^{3} - 2x^{2} - 7x + 14.

**☛ Related Questions:**

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