the cubic polynomial whose coefficient a=5 b=7 c=2 is
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Find the cubic polynomial whose zeroes are 3, 5 and -2.
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Hint: The question is related to polynomial. We have to make the cubic polynomial using the zeros given in the question. Use the sum of zeroes, product of the zeroes and sum of the product of the zero’s formula. Zeroes of the cubic polynomials are α,β,γ. Here α is equal to 3 ,β is equal to 5 and γ is equal to -2. In the cubic polynomial the coefficient of x3 is a, coefficient of x2 is b, coefficient of x is c and the consent term is d. use the formula to get your cubic polynomial equation.
Complete step by step solution:
Given that the zeroes of the cubic polynomial are 3, 5 and-2 that means (x+3),(x+5),(x−2)
We know that the zeroes of cubic polynomial is denoted by α,β,γ
Here we know that the sum of the zeroes is
sum of zeroes = coefficient of x2coefficient of x3
α+β+γ=−ba
Putting the vales of the zero in above formula
3+5−2=−bc
Solve the left-hand side
⇒6=−bc
Product of the zeroes is
product of the zeroes = consent termcoefficient of x3
α×β×γ=−da
Putting the values of the zeroes
3×5×(−2)=−da
Solve the left-hand side
⇒−30=−da
Sum of the product of zeroes is
sum of product of zeroes = coefficient of xcoefficient of x3