Question

The value of c for which the equation ax² + 2bx + c = 0 has equal roots is
(a)$\frac{b^{2}} {a}$
(b)$\frac{b^{2}} {4a}$
(c)$\frac{a^{2}} {b}$
(d)$\frac{a^{2}} {4b}$

Answer 1

SOLUTION :  

Option (a) is correct :  b²/a

Given : ax² + 2bx + c = 0

On comparing the given equation with ax² + bx + c = 0  

Here, a = a , b =  2b  , c = c

D(discriminant) = b² – 4ac

D = (2b)² - 4 × a × c

D = 4b² - 4ac

D = 4(b² - ac)

D = 0 (equal roots given)

4(b² – ac) = 0

b² - ac = 0

b² = ac  

c = b²/a  

Hence, the value of c is b²/a.

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Answer 2

Answer:

ANSWER

Given quadratic equation is ax

2

+bx+c=0

Also given b=a+c

We know that, when a given equation have equal roots, then its discriminant is always equal to be zero.

Therefore, D=0

⇒b

2

−4ac=0

⇒b

2

=4ac

⇒(a+c)

2

=4ac

⇒a

2

+2ac+c

2

=4ac

⇒a

2

−2ac+c

2

=0

⇒(a−c)

2

=0

⇒a−c=0

⇒a=c

Hence, option A is correct.