Question

8. Find m if (m - 12)x2 + 2(m - 12) x + 2 = 0 has real and equal roots.​

Answer 1

Question:

Find the value of m for which (m-12)x²+2(m-12)x+2=0 has real and equal roots

Solution:

We have,

(m-12)x²+2(m-12)+2=0

Comparing with ax²+bc+c=0,

a=m-12,b=2m-12 and c=2

Note:-

For determining whether the value of variables in an equation,we need to find the discriminant of the equation

If the discriminant D is,

•D<0,real and distinct roots

•D=0,real and equal roots

•D<0,imaginary roots

Applying the Discriminant formula,

D=b²-4ac

=[2(m-12)]²-4(m-12)(2)

=[4(m²-24m+144)]-8m+96

=4m²-96m+576-8m+96

=4m²-104m+672

Here,

Discriminant is zero [Roots are real and equal]

Thus,

4m²-104m+672=0

→m²-26m+168=0

By splitting the middle term,

→m²-12m-14m+168=0

→m(m-12)-14(m-12)=0

→(m-12)(m-14)=0

→m-12=0 and m-14=0

→m=12,14

For m=12 or 14,the given equation has real and equal roots