Question

if p and q are the zeros of the polynomial 2 x square - 7 x + 3 find the value of p square and q square​

Answer 1

$\sf{2x^{2}- 7x + 3}$

By middle term splitting,

We get,

$\implies\sf{2{x}^{2}-6x-1x+3}$

$\implies\sf{2x(x-3) - 1(x-3)}$

$\sf{(x - 3)(2x - 1)}$

Therefore, zeroes are,

x = 3 & x = 1/2

Therefore the value of p & q is 3 & 1/2 respectively.

Answer 2

Given expression:

2x^2 - 7x + 3

Sum of zeroes = -b/a

p + q = -(-7) /2

p + q = 7/2

p = 7/2 - q

Product of zeroes = c/a

pq = 3/2

(7/2 - q) q = 3/2

7/2q - q^2 = 3/2

q^2 -7/2q + 3/2 = 0

(2q^2 - 7q + 3) /2 = 0

2q^2 -6q -q +3 = 0 * 2

2q(q-3) - 1(q-3) =0

(q-3) (2q-1) = 0

q=3 or q= 1/2

p = 7/2 - 3 or p = 7/2 - 1/2

p = (7-21) /3 or p = 6/2

p = -14/3 or p = 3

So if q = 3 then p = -14/3 and if q = 1/2 then p = 3

If it's incorrect please rectify it.

Hope it helps.