Question

Find m if (m-12) x² +21m-12
real and equal roots.​

Answer 1

Question:

Find m if ;

(m-12)x^2 + 2(m-12)x + 2

has real and equal roots.

Solution;

Note: If we consider a quadratic polynomial in variable x , say;

ax^2 + bx + c .

Then,

For real and equal roots, the discriminant of the polynomial must be zero.

ie, D = 0

=> b^2 - 4ac = 0

Here, the given quadratic polynomial is;

(m-12)x^2 + 2(m-12)x + 2 = 0

Clearly, here we have;

a = m-12

b = 2(m-12)

c = 2

Thus,

For real and equal roots, we have;

=> b^2 - 4ac = 0

=> {2(m-12)}^2 - 4•(m-12)•2 = 0

=> 4(m-12)^2 - 4•2(m-12) = 0

=> (m-12)^2 - 2(m-12) = 0

=> (m-12)(m-12-2) = 0

=> (m-12)(m-14) = 0

=> (m-12) = 0 or (m-14) = 0

=> m = 12 or m = 14

Note,

Here, m=12 will be rejected, because if we put m=12 in the polynomial, then the coefficient of x^2 will become zero, and hence the given polynomial will be no more considered as a quadratic polynomial.

Thus, required value of m is 14.