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KVPY2013MathematicsQuadratic Equation

Let a, b be non-zero real numbers. Which of the following statements about the quadratic equation a x²+(a+b) x+b=0 is neccesarily true? ( I ) It has at least one negative root ( II ) It has at least one positive root. ( III ) Both its roots are real.

Options

  1. A( I ) and ( II ) only
  2. B( I ) and ( III ) only
  3. C( II ) and ( III ) only
  4. DAll of them

Correct answer

B. ( I ) and ( III ) only

Step-by-step solution

a x²+(a+b) x+b=0(x+1)(a x+b)=0 roots are -1, -b a

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