Question

if one of the root of quadratic equation is 4-√3 then another root is ​

Answer 1

Answer:

It is given that 4−i

3

is a root of the quadratic equation having real coefficients. Therefore, the other root of the equation is 4+i

3

. [Since, in a quadratic equation with real coefficients imaginary roots occur in conjugate pairs].

Now, the sum of the roots is:

(4−i

3

)+(4+i

3

)=8

And, the product of the roots is:

(4−i

3

)(4+i

3

)

=4

2

−(i

3

)

2

(∵x

2

−y

2

=(x+y)(x−y))

=16−3i

2

=16−(3×−1)(∵i

2

=−1)

=16+3

=19

Thus, the required equation is:

x

2

− (sum of the roots)x+product of the roots =0

That is,

x

2

−8x+19=0

Hence, the equation is x

2

−8x+19=0.

Step-by-step explanation:

• hope u help this