Question

if one zero of the polynomial (a+2)x2+bx+5a is reciprocal of the other, the find the value of a.

Answer 1

heya

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Answer 2

Answer:

The value of $a$ is $\frac{1}{2}$.

Step-by-step explanation:

Quadratic equations are the polynomial equations of degree two in one variable of type.

Its general form is $ax^{2} +bx+c=0$

Sum of roots is $-b/a$.

Product of roots is $c/a$.

Comparing with given equation $(a+2)x^{2} +bx+5a=0$

It is given that one root is reciprocal of other. If this is the case then,

Product of roots is unity.

Hence,

$\frac{5a}{(a+2)} =1$

$5a=a+2$

$5a-a=2$

$4a=2$

$a=\frac{2}{4}$

$a=\frac{1}{2}$

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