Question

Roots of (x-1)(x+2)+2 =0 are real or unreal

Answer 1

AnsWer :

• ( x - 1 )( x + 2 ) + 2 = 0. have real roots.

SolutioN :

We have,

$\tt : \implies(x - 1)(x + 2) = 0.$

$\tt : \implies {x}^{2} +2 x - x - 2 = 0.$

$\tt : \implies {x}^{2} + x - 2 = 0.$

★ Compare with General Equation,

$\tt \dagger \: \: \: \: \: a {x}^{2} + bx + c = 0.$

$\tt \dagger \: \: \: \: \: \red{a \neq 0.}$

Where as,

• a = 1.
• b = 1.
• c = - 2.

Let Find Nature of Roots.

• D = Discriminate.

→ D = b² - 4ac.

→ D = ( 1 )² - 4 * 1 * - 2.

→ D = 1 + 8.

→ D = 9.

• We are notice D > 0.
• according to condition roots are real.

Therefore, We say that the given equation there roots are real.