Question

Find the quadratic polynomial with the sum of 80 being -8 by 15 and product of zero being 1 by 3.​

Answer 1

Answer:

$\large\boxed{ \sf{3 {x}^{2} + 8x + 1 } }$

Step-by-step explanation:

Let, the zeroes be alpha abd beta of the quadratic equation.

Given,

Sum of zeroes = -8/3

Product of zeroes = 1/3

We know that, a quadratic polynomial is given by,

• $\sf{{x}^{2} - ( \alpha + \beta )x + \alpha \beta }$

But, according to question,

$\sf{\alpha + \beta = - \frac{8}{3} \: \: \: \: and \: \: \: \: \alpha \beta = \frac{1}{3} }$

Putting the values, we get,

$\sf{= > {x}^{2} - ( - \frac{8}{3} )x + \frac{1}{3} }\\ \\ \sf{= > 3 {x}^{2} + 8x + 1 }$