Question

check whether 3 and -5 are zeroes of the polynomial x^2-8x+15​

Answer 1

Given :

• Here, we're asked to check if 3 and -5 are the zeroes of the given Polynomial, i.e x² - 8x + 15.

So, Let's check it! ;)

If we've to know whether those two given numbers are the zeroes of the Polynomial, then we've to get 0 by substituting those numbers in place of 'x' in the given Polynomial.

Let's try & see if they're the zeroes or not ._.

By substituting 3 in place of x, we get :

$\implies{ \sf{ {x}^{2} - 8x + 15}}$

$\implies{ \sf{ {(3)}^{2} - 8(3) + 15}}$

$\implies{ \sf{9 - 24 + 15}}$

$\implies{ \sf{ - 15 + 15}}$

$\implies{ \sf{0}}$

So now, 3 is a zero of x² - 8x + 15.

And now by substituting -5 in place of x, we get :

$\implies{ \sf{ {x}^{2} - 8x + 15}}$

$\implies{ \sf{ {( - 5)}^{2} - 8( - 5) + 15}}$

$\implies{ \sf{25 + 40 + 15}}$

$\implies{ \sf{80}}$

And we know that 80 ≠ 0, Which clearly means that -5 is not a zero of x² - 8x + 15.