Question

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

Answer 1

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

If A•x^2 + B•x + C = 0 ,is any quadratic equation,

then its discriminant is given by;

D = B^2 - 4•A•C

• If D = 0 , then the given quadratic equation has real and equal roots.

• If D > 0 , then the given quadratic equation has real and distinct roots.

• If D < 0 , then the given quadratic equation has unreal (imaginary) roots...

Sᴏʟᴜᴛɪᴏɴ :-

comparing (m-12)x² + 2(m-12)x+2 = 0 with A•x^2 + B•x + C = 0 , we get ,

→ A = (m - 12)

→ B = 2(m - 12)

→ C = 2

Now, since Roots are Real and Equal, D = 0.

So,

→ D = 0

→ B² - 4AC = 0

→ [2(m - 12)]² - 4(m - 12)*2 = 0

→ 4(m - 12)² - 8(m - 12) = 0

→ 4{m² + 144 - 24m} - 8m + 96 = 0

→ 4m² - 96m - 8m + 576 + 96 = 0

→ 4m² - 104m + 672 = 0

→ 4(m² - 26m + 168) = 0

→ m² - 26m + 168 = 0

→ m² - 14m - 12m + 168 = 0

→ m(m - 14) - 12(m - 14) = 0

→ (m - 14)(m - 12) = 0

→ m = 14 & 12 .

Now, at m = 12 , the Eqn. will change into a constant num.

Hence, The value of m is 14.

Answer 2

Answer:

Solution. For real and equal roots, the Discriminant should be 0. But if m = 12, the quadratic equation will be formed hence, the vaalue of m is 14.

Step-by-step explanation: