Question

if p and q are the zeroes of the quadratic polynomial 6x^2+x-2 find the value of p^2+q^2​

Answer 1

6x² + x - 2

by splitting middle term

we get,

6x² - 3x + 4x - 2

3x (2x -1 ) + 2 (2x - 1)

(3x + 2) (2x - 1)

So,

(3x + 2) and (2x -1) are the factors of the polynomial 6x² + x - 2

so,

one zero (p) = -2/3

[ as (3x + 2) is factor 3x+2 = 0 ⇒ 3x = -2 ⇒ x = -2/3]

another zero (q) = 1/2

[ as (2x -1) is factor 2x - 1 = 0 ⇒ 2x = 1 ⇒ x = 1/2]

Now,

To be found :

p² + q²

= (-2/3)² + (1/2)²

= (4/9) + (1/4)

= (16+9)/36   [taking LCM = 36]

= 25/36 or = (5/6)²