Question

if a+ib is a root of fx=0 the the other root is
a) ib
b) a-ib
c) a
d) b

do answer is quikly please!

Answer 1

Answer:

Option B

BRAINLIEST ANSWER PLS

This will also help to solve other related sums

Step-by-step explanation:

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Study Material»IIT JEE Mathematics»Algebra»Quadratic Equations and Expressions»Discriminant of a Quadratic Equation

Discriminant of a Quadratic Equation

Quantity inside the square root (i.e. b2 – 4ac) discriminates the nature of root and so it is called discriminant (D) of the quadratic equation i.e.

D = b2 – 4ac. If you know the value of D of a given quadratic equation, you can be certain about the nature of its roots.

If D < 0 roots are complex conjugates.

If D > 0 roots are equal & real

If a, b, c Î Q (set of rational roots are real, different and rational number) and D is perfect square

If a, b, c Î Q (set of rational roots are real, different and rational number) and D is perfect irrational square

We have f(x) = ax2 + bx + c where a, b, c Î R.

Now f(x) = a

= a

= a[(x – a)(x – b)]

Where a = b = ……… (1)

These are the roots of the equation ax2 + bx + c = 0.

Now four possibilities arise :

Case I:

a, b, c are real numbers.

(i) if a > 0, then D < 0 i.e. b2 – 4ac < 0

Þ is purely imaginary

Hence from (1) both the roots a an b have to be imaginary in nature. (for conjugacy see next enquiry)

(ii) When D = 0 i.e. b2 – 4ac = 0, = 0

\ from (i) a =

Here both the roots a and b are real and equal.

Case II:

a, b, c are rational numbers.

(i) If D = b2 – 4ac is a perfect square numbers.

Then the above said roots will reduce to

Hence, the roots a and b will be real and distinct.

(ii) If D > 0 i.e. b2 – 4ac > 0 Þ would be a real number say (K). Then will be a rational numbers. Assume that if .

then a =

Here both the roots of the equation would be rational in nature.

In this way, we can know the nature of the roots of the given equation i.e. any type of quadratic equation can be solved.

Answer 2

Given; that a+ib is a root of fx=0

To Find; the other root

Solution; The complex number is a combination of real and imaginary parts. It is of the form of a+ib where a is a real part and ib is an imaginary part.

If an equation has an imaginary root then the other root should be a complex conjugate of the first number

Hence the second root is a-ib