Question

11. If the one root of the equation 4x2 – 2x + p
- 4 = 0 be the reciprocal of other. Then value
of p is

Hii Sorry all..actually I was a little busy that time so plss help me with this question..​

Answer 1

THIS IS IN THE FORM OF QUADRATIC EQUATION

IT SHOULD BE SOLVED BY USING THE TWO FOLLOWING CONDITIONS

I.THE SUM OF ROOTS OF QUADRATIC EQUATION ax^2+bx+c IS -b/a

II. THE PEODUCT OF ROOTS IS c/a

therefore by using it

the roots are x and 1/x

so by using second condition

x into 1/x=p/4

1=p/4

therefore,p=4

Answer 2

Question:

If one root of the equation 4x^2 – 2x + (p - 4) = 0 be the reciprocal of the other, then find β.

To Find:

• Value of p.

Answer:

Value of p = 8.

Solution:

Let first root = α and

Other root $= \frac{1}{a}$

The given quadratic equation:

• ${4x}{2} - 2x + (p - 4) = 0$

Here,

1. a = 4,
2. b = - 2
3. c = p - 4

We know that,

The product of roots $= \frac{c}{a}$

∴ $a \times \frac{1}{a} = \frac{p - 4}{4}$

$\implies 1 = \frac{p-4}{4}$

$\implies p-4 = 4$

$\implies p = 4+4$

$\huge \boxed{\implies 8}$

Hence,

The value of p is 8.