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Q.

If equation a x 2 +bx+c=0 has equal roots, then find ' c ' in terms of 'a' and ' b '.


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a

c = − b 2 4a

b

c = b 2 2a

c

c = b 2 4a

d

c = b 2 a  

answer is C.

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Detailed Solution

Given, the quadratic equation a x 2 +bx+c=0(a≠0) has equal roots.
We know that for a quadratic equation,
(i) If the discriminant is positive, two separate roots exist.
(ii) Both roots are equivalent if the discriminant is zero.
(iii) There are no real roots if the discriminant is negative. Instead, there are two different (non-real) complex roots.
In quadratic equation, a x 2 +bx+c=0(a≠0) Discriminant, D= b 2 −4ac .
The discriminant of given equation is,
D = (b) 2 −4(a)(c) = b 2 −4ac Let us find  ‘c’ in terms of ‘a’ and ‘b’.
For a x 2 +bx+c=0 to have equal roots, Discriminant (D) must be equal to zero. Therefore,
 If D=0 , then  b 2 −4ac=0 4ac= b 2 c= b 2 4a The value ‘c’ in terms of ‘a’ and ‘b’ if a x 2 +bx+c=0 have equal roots is b 2 4a .
The correct option is (3).
 
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If equation a x 2 +bx+c=0 has equal roots, then find ' c ' in terms of 'a' and ' b '.