Math, asked by girl6458, 4 months ago

if alpha and beta are the zeroes of the quadratic polynomial f(t)=t2-4t+3, find the value of alpha4*beta3+alpha3*beta4​

Answers

Answered by snehitha2
6

Appropriate Question :

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

Answer :

The required value of α⁴β³ + α³β⁴ is 108.

Step-by-step explanation :

Given :

α and β are the zeroes of the quadratic polynomial f(t) = t² - 4t + 3

To find :

the value of α⁴β³ + α³β⁴

Solution :

Let's find the values of α and β first.

Finding the zeroes of the polynomial f(t) = t² - 4t + 3 :

By factorization,

 t² - 4t + 3 = 0

 t² - t - 3t + 3 = 0

 t(t - 1) - 3(t - 1) = 0

 (t - 1) (t - 3) = 0

 

⇒ t - 1 = 0 ; t = 1

⇒ t - 3 = 0 ; t = 3

∴ 1 and 3 are the zeroes of the given polynomial f(t) = t² - 4t + 3.

So, let α = 1 and β = 3,

And substitute the values,

α⁴β³ + α³β⁴

[ (1)⁴ × (3)³ ] + [ (1)³ × (3)⁴ ]

[ 1 × 27 ] + [ 1 × 81 ]

27 + 81

108

The required value of α⁴β³ + α³β⁴ is 108.

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