If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.
By BYJU'S Exam Prep
Updated on: October 17th, 2023
If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, the value of α4β3 + α3β4 is 108. Candidates should write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations’ answers are the solutions to the derived equations.
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f(t) = t2 − 4t + 3, Find the Value of α4β3 + α3β4.
The question states If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.” At most, a polynomial function can have real roots equal to its degree. Set a function’s value to zero and solve to find its roots.
The polynomial zeros are the locations where the overall value of the polynomial equals zero The degree of a polynomial is the largest power of the variable x. The steps to find the value of α4β3 + α3β4 are as follows:
Since α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3.
Product of zeros = αβ = constant term/coefficient of x2 = 3
Sum of zeros = α + β = -coefficient of x/coefficient of x2 = 4
Given, α4β3 + α3β4
α3β3(α+β)
(3)3*(4) = 27 * 4 = 108
Hence, if α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, the value of α4β3 + α3β4 is 108.
Summary:
If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.
The value of α4β3 + α3β4 is 108, if α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3. Polynomial is made up of two terms, where Poly (means “many”) and Nominal (means “terms.”). The polynomial 2×2 + 5x + k indicates the addition operation. The degree of a polynomial is the highest power of the variable x. Substitute the value of the product of zeros and the sum of zeros in α3β3(α+β) and get the desired result.
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