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Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

The quadratic equation z^2+ (p+i p^ ) z+q+i q^ =0 ; where p, p^ , q, q^ are all real

Options

  1. AIf the equation has one real root then q^ 2 -p p^ q^ +q p^ 2 =0
  2. BIf the equation has two equal roots then pp ^ =2 q ^
  3. CIf the equation has two equal roots then p^2-p^ 2 =4 q
  4. DIf the equation has one real root then p^ 2 -p p^ q^ +q^ 2 =0

Correct answer

C. If the equation has two equal roots then p^2-p^ 2 =4 q

Step-by-step solution

(A) Let real root be , then ^2+ (p+i p^ ) +q+i q^ =0 ^2+p +q=0 & p^ +q^ =0 q ^ 2 p ^ 2 + p ( - q ^ p ^ )+ q =0 q ^ 2 - pp ^ q ^ + qp ^ 2 =0 (B) equal roots D=0 (p+i p^ )^2-4 (q+i q^ )=0 p^2-p^ 2 =4 q & p p^ =2 q^ then equal roots are =- p + ip ^ 2 ,- p +i p ^ 2 ; the roots will be complex.

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