Question

A quadratic polynomial whose sum and product of zeroes are 3 and 1/5 respectively is?

Answer 1

Step-by-step explanation:

Given:

Sum of zeroes = 3

Product of zeroes = 1/5

The required quadratic polynomial is:

x² - (Sum of zeroes)x + Product or zeroes = 0

⇒ x² - 3x + (1/5) = 0

Multiply by '5' to remove the denominator, we get

⇒ 5x² - 15x + 1 = 0

Hope it helps!

Answer 2

$\huge\text{\underline{Answer}}$

$\bold\red{ 5{x}^{2} - 15x + 1 }$

$\boxed{\sf{Given }}$

let the a and b be the zeroes of the quadratic polynomial.

Then,

$\bold{a + b = 3}$

$\bold{ab = \frac{1}{5}}$

$\huge\sf{solution:}$

The standard form of quadratic equation is.

$\bold{ {x}^{2} - (sum \: of \: zeroes) + (product \: of \: zeroes)}$

$\implies$ $\bold{{x}^{2} - (a + b)x + ab}$

putting the value,

$\implies$ $\bold{{x}^{2} - 3x + \frac{1}{5}= 0 }$

$\implies$ $\bold{ 5{x}^{2} - 15x + 1 =0}$

hence, the required quadratic polynomial is $\bold\red{ 5{x}^{2} - 15x + 1=0}$