Question

if a + b + c = 0, then roots of the equation 3ax 2 + 4bx + 5c = 0 are : (A) positive (B) negative (C) Real and distinct (D) imaginary

Answer 1

the Discriminant is:

D = 16b^2 - 4 * 5c * 3a = 16b^2 - 60 ac

Now a+b+c = 0, therefore, b = - (a+c)

Substituting this in D equation, we get, 

D = 16 ( -(a+c))^2 - 60ac = 16(a^2 +c^2 + 2ac) - 60 ac
= 16 a^2 + 16 c^2 + 32 ac - 60 ac 

= 16 a^2 + 16 c^2 - 28 ac

now, if a and c have different signs, (or if c = 0), then D is positive. If they have same sign, we can write this equation as: 

D = 16 a^2 + 16 c^2 - 32ac + 6 ac
= 16 (a-c)^2 + 6 ac. 

This again gives D positive. So, the roots are real and distinct. 

Ans: C

Answer 2

Answer:

Step-by-step explanation:

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