Question

The two roots of the equation x²-x+2=0 are not real is it true or false.​

Answer 1

Given that:-

The roots of the equation x² - x + 2 = 0 are not real We have to say that True or false

SOLUTION:-

The nature of roots is determined by discriminant of Quadratic equation .Discriminant of Quadratic equation is b² - 4ac .There are some cases which determine nature of roots

D> 0 Roots are real and distinct

D<0 Roots are complex and conjugate to each other

D= 0 Roots are real and equal

x² - x + 2 = 0 comparing with general form of Quadratic equation ax² + bx + c

• a = 1
• b = -1
• c = 2

D = b² - 4ac

D = (-1)² -4(1)(2)

D = 1 - 8

D = -7

Since D<0 So, roots are complex and conjugate So, the roots are no real

So, the given statement is true

Answer 2

Answer:

$\huge \bf\color{blue}{True}$

Step-by-step explanation:

$\bf \: x^{2} - x + 2 = 0$

$\bf \: Comparing \: with \: ax² + bx+c= 0,$

$\bf \: we \: get,$

$\bf \: a=1, b= -1, c= 2$

$\bf \: Therefore,$

$\bf \: D=b² - 4ac$

$\bf \: D = ( - 1)^{2} - 4(1)(2)$

$\bf \: D=1 - 8$

$\bf \: D= - 7$

$\bf = > \red {D < 0}$

Hence, the equation has two distinct real roots.