Question

if the zeroes of polynomials x²+px+q are 3and 2.Find the values of p and q and write the polynomials.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:3 \: and \: 2 \: are \: zeroes \: of \: {x}^{2} + px + q$

We know,

$\boxed{{\sf Sum\ of\ the\ zeroes=\frac{-coefficient\ of\ x}{coefficient\ of\ x^{2}}}}$

$\rm :\longmapsto\:3 + 2 = - \: \dfrac{p}{1}$

$\rm :\longmapsto\:5 = - p$

$\bf\implies \:p = - \: 5$

And,

$\boxed{{\sf Product\ of\ the\ zeroes=\frac{Constant}{coefficient\ of\ x^{2}}}}$

$\rm :\longmapsto\:2 \times 3 = \dfrac{q}{1}$

$\bf\implies \:q = 6$

Thus,

The values are

$\bf\implies \:p = - \: 5$

and

$\bf\implies \:q = 6$

And hence the required polynomial is

$\rm :\longmapsto\: f(x) = {x}^{2} - 5x + 6$