Question

Find the quadratic polynomial sum of zeros is -3 and product of the squares of zeros is 17

Answer 1

Question :-

Find the quadratic polynomial sum of zeros is -3 and product of the squares of zeros is 17.

Answer :-

$\implies \: \red{ \boxed{\bf{ {x}^{2} + 3x + \sqrt{17} }} \: }$

To find :-

Find quadratic polynomial.

Formula used :-

$\bf{ \small \ {x}^{2} - (sum \: of \: zeros) + product \: of \: zeros \: = 0}$

Step - by - step explanation :-

Given that :-

• Sum of Zeros = -3

• Product of square of Zeros = 17

Solution :-

$\bf{let \: \alpha \: and \: \beta \: are \: the \: zeros \: of \: the \: }\\ \bf{ required \: polynomial \: }$

According to the question,

$\implies \: \bf{ \alpha + \beta = - 3} \: \: .......(1) \\ and \: \\ \implies \: { \alpha }^{2} { \beta }^{2} = 17 \\ \\ \implies \: {( \alpha \: \beta )}^{2} = 17 \\ \\ \red{\bf{ taking \: square \: root \: on \: both \: sides \: }} \\ \\ \implies \: \sqrt{ {( \alpha \beta )}^{2} } = \sqrt{17} \\ \\ \implies \: \alpha \beta = \sqrt{17} \: \: \: ....(2)$

Hence,

Sum of Zeros = -3

And ,

Product of Zeros = √(17)

Therefore,

The required quadratic polynomial is ↓

$\implies \: \bf{ {x}^{2} - ( - 3)x + \sqrt{17} = 0 }\\ \\ \implies \: \boxed{\bf{ {x}^{2} + 3x + \sqrt{17} }}$

This is the required quadratic polynomial.