Question

what is the value of lesser root of the equation x^2-5x+4=0?​

Answer 1

Answer:

a and b are the roots of x^2–5x+4=0

a+b=5……………………..(1)

a.b=4…………………………(2)

Divide eq.(1) by eq.(2)

(a+b)/a.b=5/4

or 1/b+1/a=5/4………………….(3)

On reversing eq.(2) both sides

or 1/a.b=1/4 or (1/a).(1/b)=1/4…………….(4)

put (1/b)=(5/4-1/a) from eq.(3)

(1/a).(5/4–1/a)=1/4

5/4a-1/a^2=1/4

1/a^2–5/4a+1/4=0

1/a^2–1/a-1/4a+1/4=0

1/a(1/a-1)-1/4(1/a-1)=0

(1/a-1)(1/a-1/4)=0

1/a= 1 , 1/4 ,

but 1/b=(5/4–1/a)

1/b=5/4–1 ,5/4–1/4

1/b = 1/4 , ! , Answer

Answer 2

Answer:

1 is the value of lesser root of the equation $x^2 - 5x +4 = 0$

Step-by-step explanation:

Explanation:

Given in the question, $x^2 - 5x +4 = 0$.

• Middle term splitting method - The middle word is split into two parts using the procedure known as middle term factorization. We are aware that the product of prime numbers can be used to represent composite numbers.

Step 1:

we have,

$x^2 - 5x +4 = 0$

By middle term splitting method,

$x^2 - 5x +4 = 0$

⇒$x^2 - 4x-x +4 = 0$

⇒x(x -4)-1(x -4) = 0

⇒(x -4)(x -1) = 0

⇒x = 4 and x = 1

Here we can see that, 1 smaller than 4.

Final answer:

Hence, 1 is the value of lesser root of the given equation.

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