Question

If alpha and beta are the zeros of the polynomial F(x) = x^2 - px + q, then find the value of 1/alpha + 1/beta​

Answer 1

Answer:

p/q

Step-by-step explanation:

Given that :

• α and β are the zeroes of the quadratic polynomial x² - px + q.

We know that -

Quadratic polynomials are in the form of ax² + bx + c. Here,

• a = 1
• b = - p
• c = q

Sum of zeroes = $\sf \dfrac{-(coefficient \: of \: x)}{coefficient \: of \: x^2}$

⇒ α + β = $\sf \dfrac{-(-p)}{1}$

⇒ α + β = p

Product of zeroes = $\sf \dfrac{contant \: term}{coefficient \: of \: x^2}$

⇒ αβ = $\sf \dfrac{q}{1}$

⇒ αβ = q

To find :

= $\dfrac{1}{\alpha} + \dfrac{1}{\beta}$

= $\dfrac{\alpha + \beta}{\alpha \beta}$

= $\sf \dfrac{p}{q}$

Hence, the answer is p/q.