# The roots of the equation ax2 + 12x + 12 = 0 are real and equal, then a =

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The roots of the equation ax2 + 12x + 12 = 0 are real and equal, then a =
1. 1
2. 2
3. 3
4. 4

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Correct Answer - Option 3 : 3

Concept:

The roots of a quadratic equation ax2 + bx + c = 0 is give by:

$\rm x = {-b ± \sqrt{b^2-4ac} \over 2a}$

The discriminant of the equation is D = b2 - 4ac

• D > 0, roots are unequal and real
• D < 0, roots are imaginary
• D = 0, roots are real and equal

Calculation:

ax2 + 12x + 12 = 0

a = a, b = 12 and c = 12

∵ Roots are real and equal, D = 0

b2 - 4ac = 0

122 - 4 × a × 12 = 0

144 = 48a

a = 3