Question

Find the zeros of the polynomial x² – 3x - m(m +3)
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Answer 1

f(x) = x2 – 3x – m (m + 3)

By adding and subtracting mx, we get f(x) = x2 – mx – 3x + mx – m (m + 3) = x[x – (m + 3)] + m[x – (m + 3)] = [x – (m + 3)] (x + m) f(x) = 0 ⇒ [x – (m + 3)] (x + m) = 0 ⇒ [x – (m + 3)] = 0 or (x + m) = 0 ⇒ x = m + 3 or x = –m So, the zeroes of f(x) are –m and +3.

Answer 2

The zeros of the polynomial x² – 3x - m(m +3) are - m , m + 3

Given : The polynomial x² – 3x - m(m +3)

To find : The zeroes of the polynomial

Solution :

Step 1 of 2 :

Write down the given polynomial

The given polynomial is

x² – 3x - m(m +3)

Step 2 of 2 :

Find the zeroes of the polynomial

We find the zeroes of the polynomial as below

For Zeroes of the polynomial we have

$\sf {x}^{2} - 3x - m(m + 3) = 0$

$\sf \implies {x}^{2} - 3x - {m}^{2} - 3m = 0$

$\sf \implies {x}^{2} - {m}^{2} - 3x - 3m = 0$

$\sf \implies (x + m)(x - m) - 3(x + m ) = 0$

$\sf \implies (x + m)(x - m - 3) = 0$

x + m = 0 gives x = - m

x - m - 3 = 0 gives x = m + 3

So the zeroes are - m & m + 3

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