Question

if p and q are the zeroes of 3x^2+2x-9, then value of p-q is

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{p and q are zeroes of}\;\mathsf{3x^2+2x-9}$

$\underline{\textbf{To find:}}$

$\textsf{The value of p-q}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,\;3x^2+2x-9}$

$\boxed{\mathsf{Sum\;of\;zeroes=\dfrac{-b}{a}}}$

$\implies\mathsf{p+q=\dfrac{-2}{3}}$

$\boxed{\mathsf{Product\;of\;zeroes=\dfrac{c}{a}}}$

$\implies\mathsf{p\,q=\dfrac{-9}{3}}$

$\implies\mathsf{p\,q=-3}}$

$\mathsf{Now,}$

$\mathsf{(p-q)^2=(p+q)^2-4\,pq}$

$\mathsf{(p-q)^2=\left(\dfrac{-2}{3}\right)^2-4(-3)}$

$\mathsf{(p-q)^2=\dfrac{4}{9}+12}$

$\mathsf{(p-q)^2=\dfrac{4+108}{9}}$

$\mathsf{(p-q)^2=\dfrac{112}{9}}$

$\mathsf{p-q=\pm\sqrt{\dfrac{112}{9}}}$

$\therefore\boxed{\boxed{\mathsf{p-q=\pm\dfrac{4\sqrt{7}}{3}}}}$

$\underline{\textbf{Find more:}}$

if alpha and beta are the zeros of the polynomial 3x^2 - 4x - 7 then form a quadratic equation whose zeroes are 1/alpha and 1/beta

https://brainly.in/question/4436832

Answer 2

Step-by-step explanation:

answer is

p-q = + 4√3

-. _

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