Question

4. If α and β are the zeros of the quadratic polynomial f(x) = x^2 - x - 4, find the value of
1/α+1/β-αβ
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Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Solution:

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

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

⇒ α + β = - (-1)

⇒ α + β = 1

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

⇒ αβ = - 4

Now,

$\frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta \\ \\ \implies \frac{ \alpha + \beta - ( \alpha \beta ) {}^{2} }{ \alpha \beta } \\ \\ \implies \frac{1 - ( - 4) {}^{2} }{ - 4} \\ \\ \implies \frac{1 - 16}{ - 4} \\ \\ \implies \frac{ - 15}{ - 4} \\ \\ \boxed{ \therefore \: \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta = \frac{15}{4} }$