Question

If $\alpha and \beta$ are the zeros of the quadratic polynomial $p(y)= 5y^{2}-7y+1$,find the value of $\frac{1}{\alpha} +\frac{1}{\beta}$

Answer 1

Answer:

Step-by-step explanation:

SOLUTION :  

Given :  α and β are the zeroes of the quadratic polynomial. p(y)= 5y² - 7y+1

On comparing with ay² + by + c,

a = 5 , b= -7 , c= 1

Sum of the zeroes = −coefficient of x / coefficient of x²

α + β  = -b/a = -(-7)/5 = 7/5  

α + β  = 7/5 …………………(1)

Product of the zeroes = constant term/ Coefficient of x²

αβ = c/a = ⅕

αβ = ⅕……………..(2)

So,

1/α + 1/β = (α+β)/αβ  

By Substituting the value from eq 1 & eq2 , we get  

= 7/5 / ⅕  

= 7/5 × ⅕  = 7  

1/α + 1/β = 7

Hence, the value of 1/α + 1/β = 7  

HOPE THIS ANSWER WILL HELP YOU….