If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.

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 2x2 + 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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