Irrational roots

Algebra Level 2

If the equations:- a x 2 + b x + c = 0 ax^{2}+bx+c=0 And 2 x 2 + 3 x + d = 0 2x^{2}+3x+d=0 (a,b,c,d are natural numbers) Have a commen irrational root find out the value of a+b

Note:- c d = 1 \frac{c}{d}=1


The answer is 5.

Aman Sharma by Aman Sharma , 25, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Mehul Chaturvedi
Oct 19, 2014

we can compare both equations

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Aman Sharma
Oct 19, 2014

Let p + q p+\sqrt{q} be the comen root where q is a number which is not a perfect square Also coefficiants of both the equations are natural numbers so other roots of both the equations must be p − q p-\sqrt{q} hence both the roots of given equations are commen so:- a 2 = b 3 = c d \frac{a}{2}=\frac{b}{3}=\frac{c}{d} But given that c\d=1 so:- a=2 and b=3

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...