Question

find the zeros of the equation: x2+2x-15 (xsquare+2x-15)​

Answer 1

$\large{\tt{Answer\ :}}$

x² + 2x - 15

Firstly, factorise it by using middle term distribution method;

=> x² + 5x - 3x - 15

=> x (x + 5) - 3 (x + 5)

=> (x + 5) (x - 3)

Now,

x² + 2x - 15 = 0

=> (x + 5) (x - 3) = 0

x + 5 = 0

=> x = -5

x - 3 = 0

=> x = 3

So, -5 & 3 are the zeroes of polynomial x² + 2x - 15.

$\underline{\text{\large{Verification\ :-}}}$

=> x² + 2x - 15

Put x = -5

=> (-5)² + 2(-5) - 15 = 0

=> 25 -10 - 15 = 0

=> 25 - 25 = 0

=> 0 = 0

Hence, Verified ..!

Also, x² + 2x - 15 = 0

Put x = 3

=> (3)² + 2(3) - 15 = 0

=> 9 + 6 - 15 = 0

=> 15 - 15 = 0

=> 0 = 0

Hence, it is also Verified ..!

So, $\bf{-5}$ & $\bf{3}$ are the zeroes of the polynomial x² + 2x - 15.

Answer 2

$x ^{2} + 2x - 15$

$\underline\bold{\huge{SOLUTION\::}}$
Now split the middle term

To split the middle find two factor such

that their sum is 2 and product is

-15.

So, the two no's.is -3 and 5.

Because their products is -15

And sum is 2

So, Now

$x ^2+ 5x - 3x - 15$

$x(x + 5) - 3(x + 5)$

$(x + 5)(x - 3)$

Now put

$x + 5 = 0$

$x = - 5$

Again put

$(x - 3) = 0$

$x = 3$

$\underline\bold{So, the\: Zeroes\: are \:3 \:and\: -5\: :}$

$\underline\bold{\huge{Verification\: :}}$

putting in the p(X)

Replace the value of X by 3 in p(X) I,e x^2+2x-15

=3^2+2×3-15

=9+6-15

=15-15

=0

Again put the value -5 and replace the X in
x^2+2x-15
=(-5)^2+2×(-5)-15

=25-10-15

=25-25
=0

$\underline\bold{NOTE\: :}$ Zeroes of polynomial means if the value after replacing the whole p(X) is come out to be zero than that no. is called zero of a given polynomial.