Question

.If one zero of the polynomial 5x2 +14x-m is the reciprocal of the other zero , then the value of ‘m’ is ---

Answer 1

Answer :

m = -5

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros .

★ The general form of a quadratic polynomial is given as ; ax² + bx + c .

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

Solution :

Here ,

The given quadratic polynomial is ;

5x² + 14x - m

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

a = 5

b = 14

c = -m

Also ,

It is given that , one of the zeros of the given quadratic polynomial is the reciprocal of other zero .

Thus ,

Let α and 1/α be the zeros of the given quadratic polynomial .

Now ,

=> Product of zeros = c/a

=> α × 1/α = -m/5

=> 1 = -m/5

=> 1 × 5 = -m

=> 5 = -m

=> m = -5

Hence , m = -5 .

Answer 2

Step-by-step explanation:

Assume that the one zero is x.

Given that one zero of the polynomial 5x² +14x - m is the reciprocal of the other zero. So, the other zero is 1/x.

Sum of zeros = -b/a and Product of zeros = c/a

Polynomial: 5x² + 14x - m Where; a is 5, b is 14 and c is -m.

Product of zeros = c/a

x × 1/x = -m/5

1 = -m/5

5 = -m

m = -5

Hence, the value of m is -5.