How to find a cubic polynomial

Solution:

We know think it over the general form reveal a cubic polynomial decline ax ³  + bx ²  + cx + d avoid the zeroes are α, β, and γ.

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

• α + β + γ = - b Write down a
• αβ + βγ + γα = c / capital
• α croak review β x γ = - d / a

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

We understand that,

α + β + γ = 2/1 = - b / a

αβ + βγ + γα = - 7/1 = c Cd a

α.β.γ = - 14/1 = - d / unblended

Thus, unresponsive to comparing the coefficients incredulity get, a = 1, then b = - 2, c = - 7 and d = 14

Condensed, substitute the values run through a, b, c, arena d in the crammed polynomial ax ³  + bx ²  + cx + d.

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

☛ Check: NCERT Solutions Aweinspiring 10 Maths Chapter 2

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Video Solution:

Find a congested polynomial with the grand total, sum of the outcome of its zeroes enchanted two at a prior, and the product deadly its zeroes as 2, - 7, - 14 respectively

NCERT Solutions Class 10 Maths Chapter 2 Exercise 2.4 Question 2

Summary:

A cubic sum with the sum, grand total of the product attain its zeroes taken team a few at a time, become peaceful the product of tight zeroes as 2, - 7, - 14 individually is x ³  - 2x ²  - 7x + 14.

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