Question

If ∝ and β are the zeroes of the quadratic polynomial p(y) = 5y² - 7y + 1, find the value of 1/∝ + 1/β ?

Answer 1

Question :

• If ∝ and β are the zeroes of the quadratic polynomial p(y) = 5y² - 7y + 1, find the value of 1/∝ + 1/β ?

To find :

• p(y) = 5y² - 7y + 1, find the value of 1/∝ + 1/β ?

Solution :

$\: \: \: \: \: \: \: \: \: \: ↦ \tt \: a = 5, b = -7, c =1$

$\: \: \: \: \: ↦ \large\tt\alpha + \beta = \frac{ - b}{a} = \frac{ - ( - 7)}{5} = \frac{7}{5}$

$\: \: \: \: \: \: \: \: \: \: \: \: ↦ \large\tt \alpha \beta = \frac{c}{a} = \frac{1}{5} = 5$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \large\tt↦ \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha }{ \beta }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \tt↦ \frac{ \beta + \alpha }{ \alpha \beta } = \frac{7}{ \frac {5}{5}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \tt↦ \frac{ \beta + \alpha }{ \alpha \beta } = 7$

Other information :

• the first letter of the Greek alphabet (α) are know ans alpha

• In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients.

• It is defined by the integral. for complex number inputs x, y such that Re x > 0, Re y > 0.