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Let ∝ & β (α <β)  be the roots of the equation x2 + bx + c = 0
when b>0  and c < 0
If x2 -px + 4 > 0 for all real values of x, then which one of the following is correct ?
  • a)
    |P| < 4
  • b)
    |P| ≤ 4
  • c)
    |P| > 4
  • d)
     
    |P| ≥ 4
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let ∝ & β (α <β) be the roots of the equat...
Given ∝ and β are the roots of equation x2 + bx + c = 0
∴ α + β = -b
and αβ = c
As b > 0 & c < 0
So, α + β < 0
and αβ < 0
Also given that α<β⇒α<0 & β>0.
∵x2-px+4>0
Here a > 0 & f(x) > 0
∴ D < 0
∴ P-16  < 0 ⇒P2 < 16 ⇒ |P|< 4.
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Let ∝ & β (α <β) be the roots of the equation x2 + bx + c = 0when b>0 and c < 0If x2 -px + 4 > 0 for all real values of x, then which one of the following is correct ?a)|P| < 4b)|P| ≤ 4c)|P| > 4d)|P| ≥ 4Correct answer is option 'A'. Can you explain this answer?
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Let ∝ & β (α <β) be the roots of the equation x2 + bx + c = 0when b>0 and c < 0If x2 -px + 4 > 0 for all real values of x, then which one of the following is correct ?a)|P| < 4b)|P| ≤ 4c)|P| > 4d)|P| ≥ 4Correct answer is option 'A'. Can you explain this answer? for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT/PGT/PRT preparation. The Question and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus. Information about Let ∝ & β (α <β) be the roots of the equation x2 + bx + c = 0when b>0 and c < 0If x2 -px + 4 > 0 for all real values of x, then which one of the following is correct ?a)|P| < 4b)|P| ≤ 4c)|P| > 4d)|P| ≥ 4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let ∝ & β (α <β) be the roots of the equation x2 + bx + c = 0when b>0 and c < 0If x2 -px + 4 > 0 for all real values of x, then which one of the following is correct ?a)|P| < 4b)|P| ≤ 4c)|P| > 4d)|P| ≥ 4Correct answer is option 'A'. Can you explain this answer?.
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