Question

If m and n are two zeroes of the quadric polynomial f(x)=2x²-3x+7,then evaluate 1÷m+1÷n​

Answer 1

Answer :

1/m + 1/n = 3/7

Solution :

Here ,

The given quadratic polynomial is ;

f(x) = 2x² - 3x + 7

Comparing the given quadratic polynomial with the general quadratic polynomial ax² + bx + c , we have ;

a = 2

b = -3

c = 7

Also ,

It is given that , m and n are the zeros of the given quadratic polynomial f(x) .

Thus ,

=> Sum of zeros = -b/a

=> m + n = -(-3/2)

=> m + n = 3/2

Also ,

=> Product of zeros = c/a

=> mn = 7/2

Now ,

=> 1/m + 1/n = (n + m)/mn

=> 1/m + 1/n = (m + n)/mn

=> 1/m + 1/n = (3/2) / (7/2)

=> 1/m + 1/n = (3/2) × (2/7)

=> 1/m + 1/n = 3/7

Hence ,

1/m + 1/n = 3/7