Question

if p and q are the zeroes of the polynomial 4x^2-3x+2 find the value of 1/p^2+1/q^2

Answer 1

Answer:

– 7/4

Note:

If A and B are the zeros of a quadratic polynomial ax² + bx + c , then ;

Sum of zeros , (A+B) = -b/a

Product of zeros , (A•B) = c/a

Solution:

Here,

The given quadratic polynomial is :

4x² - 3x + 2

Clearly,

a = 4

b = -3

c = 2

Also,

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

Thus,

Sum of the zeros = -b/a

=> p + q = -(-3)/4 = 3/4

Also,

Product of zeros = c/a

=> pq = 2/4 = 1/2

Thus,

q² + p²

=> 1/p² + 1/q² = --------------

p²q²

p² + q²

=> 1/p² + 1/q² = --------------

p²q²

( p + q )² - 2pq

=> 1/p² + 1/q² = -------------------------

( pq )²

( 3/4 )² - 2(1/2)

=> 1/p² + 1/q² = -------------------------

( 1/2 )²

9/16 – 1

=> 1/p² + 1/q² = ----------------

1/4

( 9 – 16 )/16

=> 1/p² + 1/q² = ---------------------

1/4

– 7/16

=> 1/p² + 1/q² = -------------

1/4

– 7 × 4

=> 1/p² + 1/q² = -------------

16

=> 1/p² + 1/q² = – 7/4

Hence,

The required value of 1/p² + 1/q² = – 7/4