The roots of px^2 + qx + 2 = 0, where p and q are constants and x is a

Question

The roots of  px^2 + qx + 2 = 0 , where p and q are constants and x is a variable, are reciprocals of each other. What is the value of p?

A. -2
B. -√2
C. 0
D. 2
E. √2

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nick1816 · Answer

Product of roots = 2/p =1
p=2

LeoN88 · Answer

For ax^2 + bx + c=0 and roots m and n

m*n = c/a; So here
1 = 2/p
p=2

Rikhraj1 · Answer

Bunuel  pls explain this question.

Krunaal · Answer

Since the roots are reciprocal of each other, the product of 2 roots ( \frac{1}{r1} * r1 ) will always be 1.

Now whenever a quadratic equation of the form  ax^2 + bx + c = 0 , where a, b and c are constants is given, the product of its roots is given by  \frac{c}{a}

In the equation given to us, our  \frac{c}{a}  is  \frac{2}{p} , and since we already know that product of roots is 1 => 2/p = 1 =>  p = 2

Here's theory on  sum and product of roots

Rikhraj1 · Answer

Krunaal  sorry, still unable to understand it.

Krunaal · Answer

Can you please share which part you're not able to follow? I can then zoom into it and try to explain.

Rikhraj1 · Answer

i m not able to relate "the product of 2 roots (1/r1∗r1) will always be 1" with "the product of its roots is given by c/a".
Therefore, didn't understand this whole part "in the equation given to us, our c/a is 2/p 2, and since we already know that product of roots is 1 => 2/p = 1 => p = 2".
And this my 1st time to encounter this concept.

Krunaal · Answer

Comparing general form of quadratic equation:  ax^2 + bx + c = 0  with  px^2 + qx + 2 = 0 ; we get a = p; b = q; c = 2 .......... (i)

To calculate  product of roots  of  ax^2 + bx + c = 0 , we have a formula =>  \frac{c}{a} ......(ii) (You can memorize this formula, but if you're curious to know how it is derived, you can refer  here )

Now from (i) and (ii), you can say  product of roots  =  \frac{2}{p}  .......(iii)

The question also says that the roots are reciprocal of each other, thus when you multiply the roots you will always get 1 =>  product of roots  = 1 .......(iv)

Now from (iii) and (iv), 2/p = 1

The roots of px^2 + qx + 2 = 0, where p and q are constants and x is a

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GMAT Problem Solving (PS) Questions

The roots of px^2 + qx + 2 = 0, where p and q are constants and x is a

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards