Question

find the quadratic polynomial whose zeroes are
$\sqrt{15} and \sqrt{ - 15}$
.
​

Answer 1

There is a error in the Question :-

It should be

Find out the Quadratic polynomial whose zeros are $\sqrt{15}$ and $- \sqrt{15}$

Solution :-

As we know that any Quadratic polynomial is of the form

k( x² - Sx + P)

Where

k = constant term

S = Sum of roots

P = Product of roots

Now

Sum of roots

$= \sqrt{15} + (-\sqrt{15})$

= 0

Product of roots

$= \sqrt{15} \times (-\sqrt{15})$

$= -(\sqrt{15}^2)$

$= -15$

So our Quadratic polynomial

= k(x² - 0 + (-15))

= k(x² - 15)

Now when k = 1

$\Huge{\boxed{\sf= x^2 - 15 }}}$

Answer 2

Answer:

$\large{\underline{\boxed{\sf x^2 - 15}}}$

Step-by-step explanation:

Let α and β be the zeroes of the polynomial. Thus,

• α = √15
• β = - √15

Sum of zeroes = α + β

⇒ √15 - √15

⇒ 0

Product of zeroes = αβ

⇒ √15 * (-√15)

⇒ - 15

We know that ;

The quadratic polynomial is given by -

= x² - (α + β)x + αβ

= x² - 0x + (-15)

= x² - 15

Hence, the polynomial is x² - 15.