Question

If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.

(m – 12)x² + 2(m – 12)x + 2 = 0

Find the value of ‘m’ if the quadratic equation (m – 12)x² + 2(m – 12)x + 2 = 0 has real and equal roots.

Answer 1

Given quadratic equation is (m – 12)x² + 2(m – 12)x + 2 = 0

Comparing the above equation with ax² + bx + c = 0, we get

a = m – 12, b = 2(m – 12), c = 2

∆ = b² – 4ac

= [2(m – 12)]² – 4 × (m – 12) × 2

= 4(m – 12)² – 8(m – 12)

= 4(m² – 24m + 144) – 8m + 96

= 4m² – 96m + 576 – 8m + 96

= 4m² – 104m + 672  ...(1)

∴ m² – 26m + 168 = 0  ...(Dividing by 4 on each side)

∴ m² – 12m – 14m + 168 = 0    ....`[(168= - 14; -12),(- 14 xx -12 = 168),(- 14 - 12 = - 26)]`

∴ m(m – 12) – 14(m – 12)

∴ (m – 12) (m – 14) = 0

∴ m – 12 = 0 or m – 14 = 0

∴ m = 12 or m = 14

But, m = 12 is invalid because on taking m = 12, the coefficient of x² = m – 12

= 12 – 12

= 0

Therefore, the given equation will not be a quadratic equation.

∴ m = 14

∴ The value of m is 14.