Question

If (x-3)(3x+1)=pxsquare =+ qx +r is an identity in x, find the value of r +p - q

Answer 1

Answer:

In mathematics, a square number or perfect square is an integer that is the square of an integer;

in other words, it is the product of some integer with itself. For example, 9 is a square number, since it can be written as 3 × 3.

Answer 2

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

GIVEN

$(x - 3)(3x + 1) = p {x}^{2} + qx + r$

TO DETERMINE

$r + p - q$

EVALUATION

$(x - 3)(3x + 1) = p {x}^{2} + qx + r$

$\implies \: 3 {x}^{2} + x - 9x - 3 = p {x}^{2} + qx + r$

$\implies \: 3 {x}^{2} - 8x - 3 = p {x}^{2} + qx + r$

Comparing both sides we get

$p = 3 \: \: , \: q = - 8 \: , \: \: r = - 3$

So

$r + p - q = - 3 + 3 - 8 = - 8$

RESULT

$\red{ \fbox{THE REQUIRED ANSWER IS - 8}}$