Question

4. Find the value of 'm', if the following equation
has equal roots :
(m - 2)x2 - (5 + m)x + 16 = 0​

Answer 1

Answer: 51, 3.

Given: the following equation has equal roots: (m - 2)x² - (5 + m)x + 16 = 0

To find: the value of 'm'

Solution:

The roots of the equation: ax² + bx + c = 0 are equal when the discriminant is zero. (D = 0)

OR b² - 4ac = 0

On comparing the given equation,

a = m - 2, b = -(5 + m) and c = 16.

Therefore, Substituting,

[-(5 + m)]² - 4(m - 2)(16) = 0

(25 + m² + 10m) - 64m + 128 = 0

m² + 10m - 64m + 25 + 128 = 0

m² - 54m + 153 = 0

m² - 51m - 3m + 153 = 0

m(m - 51) - 3(m - 51)=0

(m - 51)(m - 3) = 0

m = 51 , 3

Thus, the value of m is 51, 3.

Answer 2

$\huge\tt{\bold{\underline{\underline{Question᎓}}}}$

4. Find the value of 'm', if the following equation

has equal roots :

(m - 2)x2 - (5 + m)x + 16 = 0

$\huge\tt{\bold{\underline{\underline{Answer᎓}}}}$

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The given equation is given in the quadratic form hence,we used quadratic formula to find out the roots.

=>The roots of the equation :ax^2+bx+c=0 are equal when the discriminant is zero(D=0)

$\bold{\boxed{\blue{=>D= {b}^{2} - 4ac = 0}}}$

on comparing the coefficient with D.

a=m-2;b=-(5+m) & c=16

$= > - {[(5 + m)]}^{2} - 4(m - 2)(16)$

$= > (25 + {m}^{2} + 10m)( - 4m + 8)(16)$

$= > {m}^{2} + 10m - 64m + 25 + 128 = 0$

$= > {m}^{2} - 54m + 153 = 0$

$= > m(m - 51) - 3(m - 51) = 0$

$= > (m - 51)(m - 3) = 0$

$\bold{\red{\boxed{= > m = 51,3}}}$

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