Question

if p and q are the zeroes of the quadratic polynomials 2x^3+3x+5find value of 1/p+1/q​

Answer 1

Answer:

1/p + 1/q = –3/5

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 .

★ 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

★ If α and ß are the zeros of any quadratic polynomial , then it is given by ;

x² - (α + ß)x + αß

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then they (α and ß) are also the zeros of the quadratic polynomial k(ax² + bx + c) , k≠0.

Solution:

Here,

The given quadratic polynomial is ;

2x² + 3x + 5 .

Clearly,

a = 2

b = 3

c = 5

It is given that , p and q are the zeros of the given quadratic polynomial .

Thus,

Sum of zeros = -b/a

p + q = -3/2

Also,

Product of zeros = c/a

pq = 5/2

Thus,

1/p + 1/q = (q + p)/pq

= (p + q)/pq

= (-3/2)/(5/2)

= (-3/2)×(2/5)

= -3/5

Hence,

Required answer is (-3/5) .