Question

3.
If the roots of the equation
X? - bx
ax-c
m-1
m +1
- are equal and of opposite sign, then the value of m will be
a-b
a+b
b-a
a + b
a + b
a-b
bta
b-a​

Answer 1

Answer:

root are equal and opposite put sum of root =zero u will get ur answer

Answer 2

Answer:

Option (A) - $\large{\underline{\boxed{\sf m = \dfrac{a - b}{a + b}}}}$

Step-by-step explanation:

Given that ;

The roots of the given equation are equal but of opposite signs. Thus, the factorisation must be equal to (ax + b)(ax - b). Also, the middle term of quadratic equation must be zero.

Here's the equation -

★ $\bf \dfrac{x^2 - bx}{ax - c} = \dfrac{m - 1}{m + 1}$

On cross-multiplying -

(m + 1)x² - (m + 1)bx = (m - 1)ax - c(m - 1)

⇒(m + 1)x² - (m + 1)bx - (m - 1)ax + c(m - 1) = 0

⇒ (m + 1)x² - x[(m + 1)b + (m - 1)a] + c(m - 1) = 0

Now, it is of the form ax² + bx + c = 0.

Here, bx = 0

⇒ (m + 1)b + (m - 1)a = 0

⇒ bm + b + am - a = 0

⇒ bm + am = a - b

⇒ m(a + b) = a - b

⇒ m = $\sf \dfrac{a - b}{a + b}$

Hence, option (A) is correct!