Question

if α,β are the zeroes of quadratic polynomial f(x)=xsquare-x-4 find the value of 1/α+1/β-αβ​

Answer 1

Step-by-step explanation:

This is the answer of this question.

Answer 2

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☞ Your Answer is 15/4

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$\huge\sf\blue{Given}$

☆ α and β are the zeros of x²-x-4

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✭ 1/α+1/β-αβ

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Given polynomial ;

f(x) = x² - x - 4

On comparing the given equation with ax² + bx + c = 0, we get -

◕ a = 1

◕ b = - 1

◕ c = - 4

$\sf Sum \ of \ zeroes = - \dfrac{b}{a}$

➢ α + β = - (-1)

➢ α + β = 1

$\sf Product \ of \ zeroes =\dfrac{c}{a}$

➝ αβ = - 4

Now,

$\sf\frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta \\ \\ \sf\dashrightarrow \frac{ \alpha + \beta - ( \alpha \beta ) {}^{2} }{ \alpha \beta } \\ \\ \sf\dashrightarrow \frac{1 - ( - 4) {}^{2} }{ - 4} \\ \\ \sf\dashrightarrow \frac{1 - 16}{ - 4} \\ \\ \sf \dashrightarrow \frac{ - 15}{ - 4}$

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