Question

if A and B are the zeros of the polynomial p x square - 2 X + 3 P and a + b equal to ab then P is​

Answer 1

Answer

The required value of p is 2/3

${\large{ \bf\underline{Given : }}}$

The quadratic polynomial is

• px² - 2x + 3p
• a and b are the zeroes of the polynomial also a + b = ab

$\bf \underline{ \large{To \: Find : }}$

• The value of p

$\bf \large \underline{Solution : }$

We have the quadratic polynomial :

px² - 2x + 3p

and its zeroes a and b

Now from relationship of zeroes and polynomials

$\sf sum \: of \: the \: zeroes = - \dfrac{coefficient \: of \: {x}}{coefficient \: of \: {x}^{2} } \\ \\ \sf \implies a + b = - \frac{ - 2}{p} \\ \\ \sf \implies a + b = \frac{2}{p}$

Again , we have from product relation of zeroes and coefficients :

$\sf product \: of \: zeroes = \dfrac{constant \: term}{coefficient \: of \: {x}^{2} } \\ \\ \implies \sf ab = \frac{3p}{p} \\ \\ \implies \sf ab = 3$

Since , we were given :

$\sf \implies a + b = ab \\ \\ \implies \sf \dfrac{2}{p} = 3 \\ \\ \implies \sf 2 = 3p \\ \\ \implies \sf p = \dfrac{2}{3}$

Therefore , the value of p is 2/3