Question

Q.8 A quadratic polynomial with 3 and 2 as the sum and product of its zeros respectively is

Answer 1

$\bf\huge\blue{\underline{\underline{ Question : }}}$

A quadratic polynomial with 3 and 2 as the sum and product of its zeros respectively is.

$\bf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• Sum and Product of zeroes of a Quadratic Polynomial are 3 and 2.

★ To find,

• Quadratic Polynomial.

★ Let,

$\tt\:\rightarrow Sum\:of\:the\:zeroes : \alpha + \beta = -\cfrac{b}{a}$

$\tt\:\rightarrow Product\:of\:the\:zeroes : \alpha \beta = \cfrac{c}{a}$

★ Now,

The form of a Quadratic Polynomial is :

$\orange{\bigstar}\boxed{\rm{\red{ x^{2} -(\alpha + \beta)x +\alpha\beta = 0 }}} \orange{\bigstar}$

• Substitute the zeroes.

$\sf\:\implies x^{2} - (3)x + 2 = 0$

$\sf\:\implies x^{2} - 3x + 2 = 0$

$\underline{\boxed{\rm{\purple{\therefore Hence,\:the\:Quadratic\:Polynomial\:is\:x^{2}-3x+2=0.}}}}\:\orange{\bigstar}$