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 ax³ + bx² + 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 ax³ + bx² + 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 ax³ + bx² + cx + d.

Hence the polynomial is x³ - 2x² - 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 x³ - 2x² - 7x + 14.

☛ Related Questions:

• If the zeroes of the polynomial x^3 - 3x^2 + x + 1 are a - b, a, a + b, find a and b.
• If two zeroes of the polynomial x^4 - 6x^3 - 26x^2 + 138x - 35 are 2 ± √3 find other zeroes.
• If the polynomial x4 - 6x3 + 16x2 - 25x + 10 is divided by another polynomial x2 - 2x + k, the remainder comes out to be x + a, find k and a.
• Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also, verify the relationship between the zeroes and the coefficients in each case:(i) 2x3 + x2 - 5x + 2; 1/2, 1, - 2(ii) x3 - 4x2 + 5x - 2; 2, 1, 1