Question

if the one root of the equation 4x2-2x+p-4=0 be the recipocal of other than find the value of p​

Answer 1

EXPLANATION.

one roots of the equation = 4x² - 2x + p - 4 = 0.

be reciprocal to other.

To find the value of p.

Let the roots of equation be = a.

The roots is reciprocal to other = 1/a.

products of zeroes of quadratic equation.

→ ab = c/a

→ a X 1/a = p - 4 / 4

→ 1 = p - 4 / 4

→ 4 = p - 4

→ p = 4 + 4

→ p = 8.

More information.

General equation of quadratic equation.

= ax² + bx + c.

Sum of zeroes of quadratic equation.

= a + b = -b/a.

products of zeroes of quadratic equation.

= ab = c/a.

quadratic equation formation.

= x² - ( a + b) x + ab.

Discriminant = b² - 4ac.

Answer 2

✯ Given :-

◩The one roots of the equation is 4x² - 2x + p = 0 be the reciprocal of the other.

✯ To Find :-

◩ What is the value of p.

✯ Solution :-

» Let, the roots of the equation be a

» And, there reciprocal will be $\dfrac{1}{a}$

➙ Given :

$\mapsto$ 4x² - 2x + p = 0

where, a = 4, b = - 2, c = p

We know that,

$\boxed{\bold{\large{αβ\: =\: \dfrac{c}{a}}}}$

According to the question by using the formula we get,

⇒ αβ = $\dfrac{c}{a}$

By putting the value we get,

⇒ a × $\dfrac{1}{a}$ = $\dfrac{p - 4}{4}$

⇒ 1 = $\dfrac{p - 4}{4}$

⇒ p - 4 = 4

⇒ p = 4 + 4

➥ p = 8

$\therefore$ The value of p is 8 .