Question

Equation ax^(2)+2x+1 has one double root if (1) a=0 (2) a=-1 (3) a=1 (4) a=2

Answer 1

$Compare \: given \: Quadratic \: equation$

$with \: Ax^{2} + Bx + C = 0 , we \:get$

$A = a , B = 2 \: and \: C = 0$

$\pink{ Discreminant (D) = 0 }$

$\blue {( Given \: it \:has \: equal \:roots ) }$

$\implies B^{2} - 4AC = 0$

$\implies 2^{2} - 4 \times a \times 1 = 0$

$\implies 4 - 4a = 0$

$\implies - 4a = - 4$

$\implies a = \frac{-4}{-4}$

$\implies a = 1$

Therefore.,

$Option \green { ( 3 ) } \: is \: correct.$

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Answer 2

Option (3) a = 1 .

Solution :-

Given that, ax² + 2x + 1 = 0

Compare given quadratic equation with ax² + bx + c = 0. we get,

a = a , b = 2 , c = 1

=> Δ ( Discreminant) = 0

=> b² - 4ac = 0

=> 2² - 4 × a × 1 = 0

=> 4 - 4a = 0

=> -4a = -4

=> a = -4 / -4

=> a = 1 .