Question

Find p for which the quadratic equation x²+px+1=0 has real roots.​

Answer 1

Step-by-step explanation:

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Class 11

>>Maths

>>Complex Numbers and Quadratic Equations

>>Quadratic Equations

>>Prove that the equation x^2 + px - 1 = 0

Question

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Prove that the equation x

2

+px−1=0 has real and distinct roots for all real values of p.

Hard

Solution

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To prove: The equation x

2

+px−1=0 has real and distinct roots for all real values of p.

Consider x

2

+px−1=0

Discriminant D=p

2

−4(1)(−1)=p

2

+4

We know p

2

≥0 for all values of p

⇒p

2

+4≥0 (since 4>0)

Therefore D≥0

Hence the equation x

2

+px−1=0 has real and distinct roots for all real values of p.

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Answer 2

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