Question

If the roots of the equation 6x² - 13x + m=0 are reciprocal
of each other, find the value of m.​

Answer 1

Solution

Given :-

• Equation is , 6x² - 13x + m = 0,
• Reciprocal of roots each other.

Find :-

• Value of m

Explanation

Let,

• P & q be root of this Equation

According to question,

• p = 1/q______________(1)

Using Formula

★ Sum of roots = _(coefficient of x)/(coefficient of x²)

★product of roots = (Constant part)/(coefficient of x²)

Now, Calculate

==> Sum of roots = -(-13)/6

==> p + q = 13/6__________(2)

==> 1/p+ q = 13/6

==> (1+q²)/q = 13/6

==> 6 + 6q² - 13q = 0

==> 6q² - 13q + 6 = 0

==> 6q² - 9q - 4q + 6 = 0

==> 3q (2q - 3)- 2(2q - 3) = 0

==> (3q - 2)(2q - 3) = 0

==> 3q - 2 = 0 Or, 2q - 3 = 0

==> q = 2/3 Or, q = 3/2

Keep Value of q in equ(1)

When,

• q = 2l3

==> p = 1/q = 3/2

and,

When,

• q = 3/2

then,

==> p = 2/3

Now, Calculate Value of m

==> product of roots = m/6

==> p . q = m/6

• p = 1/q

==> 1/q × q = m/6

==> m/6 = 1

==> m = 6

Hence

• Roots of Equation will be 2/3 , 3/2 or 3/2 , 2/3
• Value of m = 6

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