Question

Find the relation between p and q if on root of x+px+q=0,is 37 times the other root

Answer 1

Answer:

37p² = 1444q  

Step-by-step explanation:

Given :

One root of x² + px + q = 0 is 37 times the other root.

To find :

the relation between p and q

Solution :

For the given polynomial,

• x² coefficient = 1
• x coefficient = p
• constant = q

Let α and β are the roots of the given quadratic equation.

One root is 37 times the other root.

β = 37α

We know,

⇒ Sum of roots = -(x coefficient)/x² coefficient

⇒ Product of roots = constant/x² coefficient

So,

Sum of roots = -p/1

α + β = -p

α + 37α = -p

 38α = -p

   α = -p/38

Product of roots = q/1

 α × β = q

 α × 37α = q

 37α² = q

 37(-p/38)² = q

  37p²/1444 = q

  37p² = 1444q

The required relation between p and q is 37p² = 1444q