Question

If a and b are the zeros of the quadratic polynomial f(x)=5x2-7x+1,find the value 1/a+1/b

Answer 1

Answer:

$\text{The value of }\frac{1}{a}+\frac{1}{b}\text{ is 7}$

Step-by-step explanation:

Given that if a and b are the zeros of the quadratic polynomial

$f(x)=5x^2-7x+1$

$\text{we have to find the value of }\frac{1}{a}+\frac{1}{b}$

$f(x)=5x^2-7x+1$

$\text{sum of zeroes=}a+b=\frac{-b}{a}=\frac{7}{5}$

$\text{Product of zeroes=}abc=\frac{c}{a}=\frac{1}{5}$

Now,

$\frac{1}{a}+\frac{1}{b}$

$\frac{b+a}{ab}$

$\frac{\frac{7}{5}}{\frac{1}{5}}=7$

$\text{The value of }\frac{1}{a}+\frac{1}{b}\text{ is 7}$