# 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:**

To solve this question, follow the steps below.

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

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

Put the values of the known coefficients, you will get the value of the unknown coefficient.

Now put the values of coefficients in the general equation of the cubic polynomial ax^{3} + bx^{2} + cx + d.

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

αβ + βγ + γα = - 7/1 = c/a

α.β.γ = - 14/1

= - d / a

If a = 1, then b = - 2, c = - 7 and d = 14

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

**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:

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

The polynomial x^{3} - 2x^{2} - 7x + 14 is the required cubic polynomial where the sum, sum of the product of its zeroes taken two at a time and the product of its zeroes are 2, –7, –14 respectively