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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

667. If m and n are the roots of the equation

, find the value ofIt is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

.

668. If m and n are the roots of the quadratic equation

, find the value ofIt is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

Solution #668 The value of (m/n) +(n/m) is 3(√5)

*Last edited by 666 bro (2020-01-14 01:52:35)*

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

669. Find the value of p for which the quadratic equation

has equal roots.It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

670. Find the value of p for which the quadratic equation

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

671. Find the value of 'p' for which the quadratic equation have equal roots:

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

672. For what positive values of 'm', the roots of the following equation is

(1) equal

(2) distinct

(3) imaginary.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

673. For what values of 'm', the roots of the following equation are

(1) equal

(2) distinct

(3) imaginary.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

674. Find the roots of the quadratic equation:

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

675. Find the roots of the quadratic equation:

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

Solution for # 675 is x= - √2 , x= -(5/√2)

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi 666 bro,

Excellent!

676. Find two consecutive positive integers, sum of whose squares is 365.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

#676 : The two consecutive numbers are 13 and 14 respectively.

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

The solution 676 is correct. Good work!

677. Find the positive values of m if the roots of the equation is

are(a) equal

(b) distinct

(c) imaginary.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

(a ) for equal roots m = 6.

(b) for distinct roots m > 6.

(c) for imaginary roots m < 6.

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

Good work!

678. Find the value of p for which the quadratic equation given below have equal roots.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

#678: the value of p = ±2√(2).

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Good work!

679. Find the value of p for which the quadratic equation given below have equal roots.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

The value of p = 1/3.

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Neat work!

680. A and B are mutually exclusive events such that

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

p(AUB) = (31/35).

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Well done!

681. In a random experiment, there is a chance of win or lose. But the probability of winning is four times of losing. Find the probability of winning.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

P(winning) = 4/5 .

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Good work!

682. Two dice are thrown simultaneously. Find the probability of getting

(a) same number on both faces and

(b) both faces having multiples of 5.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**pi_cubed****Member**- From: A rhombicosidodecahedron
- Registered: 2020-06-22
- Posts: 61

If both conditions are satisfied then P(a and b) = 1/36

(Correct me if I'm wrong, it seems too simple.)

*Last edited by pi_cubed (2020-07-01 01:02:24)*

e to the i pi plus 1 is zero -Leonhard Euler | a squared plus b squared equals c squared -Pythagoras | Energy equals mass times the speed of light squared -Albert Einstein | i² = -1 | x^2+1=0 x^2=-1 x=i

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