Question

The zeroes of the polynomial x2-3x - m (m + 3) are
(a) m,m +3 (b) -m, m +3 (c) m,-(m + 3)
(d) -m,-(m+3)
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Answer 1

Answer:

x² -3x - m(m + 3) = 0

=> x² -3x -m² -3m =0

=> x² - m² - 3x - 3m = 0

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

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

=> x + m = 0 , or , x - m - 3 =0

=> x = - m or, x = m + 3

so the correct answer is option b

Answer 2

Given:

The zeroes of the polynomial x2-3x - m (m + 3) are

To Find:

(a) m, m +3

(b) -m, m +3

(c) m,-(m + 3)

(d) -m,-(m+3)

Solution:

We can the zeroes of this polynomial by using different methods like quadratic formula rule or by splitting the middle term with x as a variable, here we will be using the quadratic formula which goes as for a polynomial ax^2+bx+=0

$x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}$

So using this formula and putting all the values from the given equation we will have,

$x=\frac{3\pm \sqrt{9+4m^2+12m} }{2}\\=\frac{3\pm \sqrt{(2m+3)^2} }{2}\\=\frac{3\pm (2m+3)}{2}\\=(m+3) , -m$

So we will be getting two roots or zeroes of the polynomial as (m+3) and -m

Hence, the correct option will be (c).