NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice

If a , b , c are real numbers satisfying the condition a + b + c = 0, then the roots of the quadratic equation 3 a x 2 + 5 b x + 7 c = 0 are

Options

APositive
Bnegative
Creal and equal
Ddistinct but not imaginary

Correct answer

D. distinct but not imaginary

Step-by-step solution

D = 25 b 2 - 4 × 3 a × 7 c = 25 - a - c 2 - 84 a c = 25 a 2 + c 2 + 2 a c - 84 a c = 25 a 2 + c 2 - 34 a c = 17 a 2 + c 2 - 2 a c + 8 a 2 + c 2 = 17 a - c 2 + 8 a 2 + c 2 D > 0 ⇒ Roots are real and distinct

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