Question

if and bare the zeroes of the polynom5x²-7x+2 then sum of their reciprocals is​

Answer 1

Step-by-step explanation:

isko ham gudankhand vidhi dwara HAL karenge

Answer 2

$\mathbb{\bold{ANSWER}}$

Sum of reciprocals of zeroes = 7/2

$\mathbb{\bold{EXPLANATION}}$

Let, p(x) = 5x² - 7x + 2 and having zeroes a and b

We have to find,

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

We know that,

for a polynomial of the form px² + qx + r having zeroes a and b

Sum of zeroes of polynomial = a + b = -q/p

Product of zeroes of polynomial = ab = r/p

In the given case,

p = 5

q = -7

r = 2

Therefore,

a + b = -q/p

a + b = -(-7)/5

a + b = 7/5

ab = r/p

ab = 2/5

Substituting the values in sum of reciprocals we get,

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

$\implies$ $\frac{\frac{7}{5} }{\frac{2}{5} } =\frac{7 \times5}{2 \times 5} =\frac{7}{2}$