Question

If p and q are zero of polynomial p(x) =x2-5x+6 then the value of p +q-3pq

Answer 1

Question :–

• If p and q are zero of polynomial p(x) = x² - 5x + 6 then the value of p + q - 3pq.

ANSWER :–

$\\ { \red{ \longrightarrow{ \boxed{ \bold{ p + q - 3pq \: = \: - 13 }}}}}$

GIVEN :–

• A quadratic polynomial x² - 5x + 6 = 0 which have two roots p and q.

TO FIND :–

• Value of p + q - 3pq = ?

SOLUTION :–

• According to the question –

$\\ \implies{ \bold{ {x}^{2} - 5x + 6 = 0}}$

$\\ \implies{ \bold{ {x}^{2} - 3x - 2x+ 6 = 0}}$

$\\ \implies{ \bold{ x(x - 3) - 2(x - 3) = 0}}$

$\\ \implies{ \bold{ (x - 2)(x - 3) = 0}}$

$\\ \implies{ \bold{ x = 2 \: \: , \: \: x = 3}}$

So that p = 2 and q = 3.

• Now let's find –

$\\ \: \: \: \: \: { \bold{ = \: p + q - 3pq }}$

$\\ \: \: \: \: \: { \bold{ = \: 2 + 3 - 3(2)(3) }}$

$\\ \: \: \: \: \: { \bold{ = \: 5 - 3(6) }}$

$\\ \: \: \: \: \: { \bold{ = \: 5 -18 }}$

$\\ \: \: \: \: \: { \bold{ = \: - 13 }}$

Hence , ${ \red { \boxed{ \bold{ p + q - 3pq \: = \: - 13 }}}}$

Answer 2

✯✯ QUESTION ✯✯

If p and q are zero of polynomial $p(x) ={x}^{2}-5x+6$ then the value of $p +q-3pq$.

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✰✰ ANSWER ✰✰

$⇝{x}^{2}-5x+6$

By Splitting Middle Term : -

$⇝{x}^{2}-5x+6=0$

$⇝{x}^{2}-(3x+2x)+6=0$

$⇝{x}^{2}-3x-2x+6=0$

$⇝x(x-3)-2(x-3)$

$⇝(x-2) (x-3)$

$⇝\textbf{x=2\:and\:x=3}$

So,p=2 and q=3

➜Putting Values in p+q-3pq

$⇝2+3-3(2)(3)$

$⇝5-3(6)$

$⇝5-18$

☛$\large{\boxed{\bold{\bold{\red{\sf{-13}}}}}}$