Question

If one of the zeroes of
ax^2 + (a-4)x + 3,
is the reciprocal of the other, then find 'a'

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Answer 1

Answer:

Hello guys ,here is the solution of this one . This types of questions are simply done by products of zeroes always remember this one.

Answer 2

$\LARGE{\bf{\underline{\underline{GIVEN:-}}}}$

• The two roots of ax² + (a - 4)x + 3 are reciprocal of each other.

$\LARGE{\bf{\underline{\underline{TO \ FIND:-}}}}$

• The value of a.

$\LARGE{\bf{\underline{\underline{SOLUTION:-}}}}$

Let one roots be α.

Then the second root will be 1/α [The one zero is reciprocal of the other.]

Now, in ax² + (a - 4)x + 3,

• Coefficient of x² = a
• Coefficient of x = a - 4
• Constant = 3

Then, we know that:

$\boxed{\sf{\blue{Product \ of \ roots = \dfrac{Constant}{Coefficient \ of \ x^2} }}}$

Substitute the values.

$\to \sf \not{\alpha} \times \dfrac{1}{\not{\alpha}} = \dfrac{3}{a}$

$\to \sf \dfrac{3}{a} =1$

$\leadsto \sf{\red{a=3}}$

The value of a is 3.