Question

kindly help me with question no. 2, (v) and (vi) part..
plz give full explanation.
In my answer I am getting 1/4 (xsquare+ x++ 1) . But in NCERT it is 4xsquare+ 4x+1. So I want to learn how to remove the denominator and multiply it above.
Kindly help!!

Answer 1

Here is the solution :

In general, if the roots of a Quadratic equation is a and b, Then the Quadratic equation is

x² - (a+b)x + ab = 0,

Now ,

(v) :
Sum of the roots = -1/4 = a+b,
Product of the roots = 1/4 = a+b,

Now,
The quadratic equation will be,
x² -(-1/4)x + 1/4 = 0,
Multiplying 4 on both sides,

=> 4x² + 1x + 1 = 0,
[Since 1x² * 4 = 4x², 1/4x * 4 = 1x, 1/4*4 = 1 ]

(vi) :
Sum of the roots = 4 = a+b,
Product of the roots = 1 = ab,

=> The Quadratic Equation will be,
x² -(4)x + 1 = 0,
=> x² - 4x + 1 = 0 !

Therefore : (v) : 4x² + x + 1 = 0,
(vi) x² - 4x + 1 = 0.

Hope you understand, Have a great day !
Thanking you, Bunti 360 !