Question

two roots of x²-(a+b)x + ab=0 (a,b are rational)are___
(a) not real
(b) real and rational
(c) real and irrational
(d) cannot be determined
please solve this Asap​

Answer 1

Answer:

option d)

Step-by-step explanation:

hope it will help you

Answer 2

Given :-

• A quadratic equation x²-(a+b)x + ab=0

To Find :-

• Nature of roots

Concept Used :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

• If Discriminant, D > 0, then roots of the equation are real and unequal.

• If Discriminant, D = 0, then roots of the equation are real and equal.

• If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

• Discriminant, D = b² - 4ac

Let's solve the problem now!!!

Given quadratic equation is

$\rm :\longmapsto\: {x}^{2} - (a + b)x + ab = 0$

Its Discriminant, D is evaluated as

$\rm :\longmapsto\:Discriminant, D = {\bigg( - (a + b) \bigg) }^{2} - 4ab$

$\rm :\longmapsto\:D = {\bigg( (a + b) \bigg) }^{2} - 4ab$

$\rm :\longmapsto\:D = {a}^{2} + {b}^{2} + 2ab - 4ab$

$\rm :\longmapsto\:D = {a}^{2} + {b}^{2} - 2ab$

$\rm :\longmapsto\:D = {(a - b)}^{2}$

$\bf\implies \:Discriminant, D > 0 \: and \: perfect \: square$

$\bf\implies \:Roots \: are \: real \: and \: rational.$

$\boxed{ \bf \: Hence, \: option \: (b) \: is \: correct}$