Question

If pand q are the zeroes of the polynomial 2x2- 3x -2 ,then find the value of P2 + q2

Answer 1

Step-by-step explanation:

the answer is in the picture.

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

If $\alpha \: \: and \: \: \beta \:$are the zeroes of the quadratic polynomial $a {x}^{2} + bx + c$

Then

$\displaystyle \: \alpha + \beta \: = - \frac{b}{a} \: \: and \: \: \: \alpha \beta \: = \frac{c}{a}$

CALCULATION

The given Quadratic polynomial is

$2 {x}^{2} - 3x - 2$

Comparing with

$a {x}^{2} + bx + c$

We get

$a = 2 , b = - 3 , c = - 2$

Since P & q are the zeros of the given Quadratic polynomial

So

$\displaystyle \: \: p + q \: = \frac{3}{2} \: \: \: and \: \: pq \: = - \frac{2}{2} = - 1$

Hence

${p}^{2} + {q}^{2}$

$= {(p + q)}^{2} - 2pq$

$\displaystyle \: = ( { \frac{3}{2} )}^{2} - 2 \times ( - 1)$

$= \displaystyle \frac{9}{4} + 2$

$= \displaystyle \frac{17}{4}$