Question

If 3 is a zero of the polynomial x²+2x-a find the value of 'a', and the other zero

Answer 1

Here, f(x) = x² + 2x - a

3 is the zero of the polynomial, then f(3) = 0

f(3) = 0

(3²)+2(3)-a= 0

9 + 6 - a= 0

15 - a = 0 .

15 = a.

$\boxed {a = 15}$

Now, The polynomial is x² + 2x - 15 .

Factorising the polynomial,

x² + 2x - 15

x² + 5x - 3x - 15

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

( x + 5 ) ( x - 3 )

Therefore , x²+2x-15 = (x+5)(x-3)

Zero of the polynomial : The value of the variable for which polynomial is 0

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

x = -5 , x = 3 .

Therefore, the other zero is -5 .

Answer 2

Hi there !!
Here's your answer

Given that ,
3 is one of the zero of the polynomial
x² + 2x - a

so,
x = 3

p(3) = (3)² + 2(3) - a = 0
9 + 6 - a = 0
-a = 0 - 15
-a = -15
a = 15

Thus,
the value of a is 15

Also,
we need to find the other zero

We have the polynomial
x² + 2x - 15
Factorising by splitting the middle term,
we have,
x² + 5x - 3x - 15
Taking out common factors,
we have,
x(x + 5) - 3(x + 5)
Taking (x + 5) as a common factor,

we have,


(x + 5)(x - 3) = 0
x = 3 [ given ]and x = -5

So,
the other zero is -5

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Hope it helps :D