Question

2) Find the quadratic polynomial with the given number as the sum and product of its zero
respectively 1/5


and -2.
​

Answer 1

Answer:

To find the Quadratic Polynomial when sum and product of zeroes are given:

we use the formula:  x^2-[sum of zeroes]*x + Product of zeroes

Step-by-step explanation:

Here we know what the sum of zeroes and product of zeroes are ,

So, the the quadratic equation is,

x^2-[1/5]x+[-2]

But, we find that there is a fraction here, we need to remove the denominator.

We multiply 5 throughout the polynomial to remove the denominator 5 .

5 [x^2-[1/5]x+[-2]

=> 5x^2-x-10 is the final quadratic equation

Hope it helps :)

Answer 2

Step-by-step explanation:

$Let, \: \alpha \: and \: \beta \: be \: the \: zeroes \: of \: the \: polynomial$

$\boxed{ \huge\mathfrak{ \colorbox{gray}{Given :-}}}$

$: \implies \: sum \: of \: zeroes \: (\alpha + \beta) = \frac{1}{5}$

$: \implies \: product \: of \: zeroes \: (\alpha + \beta) = - 2$

$\huge{ \mathfrak{We \: know \: that,}}$

${x}^{2} - ( \alpha + \beta )x + ( \alpha \times \beta ) = 0$

${x}^{2} - ( \frac{1}{5})x - 2 = 0$

$5 {x }^{2} - x - 10 = 0$

$5 {x }^{2} - x - 10 = 0 \: this \: is \: the \: required \: polynimal$