Question

The quadratic equation x2 -x-2=0 has roots which are: (a) Real and equal (b) Real, unequal and rational (c) Real, unequal and irrational (d) Not real​

Answer 1

Answer:

(b) Real, unequal and rational.

Explanation:

Given equation,

$\rm \implies \: {x}^{2} - x - 2 = 0$

On comapring with the general form of a quadratic equation ax² + bx + c = 0

We get,

• a = 1
• b = -1
• c = -2

Finding discriminant :-

$\rm \longrightarrow \: D = {(b)}^{2} - 4ac$

Substituting the values,

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

$\rm \longrightarrow \: D = 1 - ( - 8)$

$\rm \longrightarrow \: D = 1 + 8$

$\rm \longrightarrow \: D = 9$

∴ Discriminant of the equation is 9

Since, D = 9 > 0 and also is a perfect square.

The nature of roots of the equation is real, unequal and irrational.

Answer 2

Answer:

The nature of the roots of the quadratic equation $x^{2} -x-2=0$ are real, unequal, and irrational

Step-by-step explanation:

• A quadratic equation is a type of equation whose degree is two, a quadratic equation can be represented as

                            $ax^{2} +bx+c=0$

• the corresponding root or the value of x that satisfies the quadratic equation is given by the formula

                 $x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}$     or $x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

From the question, we have given a quadratic equation of the form

$x^{2} -x-2=0$

as compared with the standard equation we get

$a=1\\b=-1\\c=-2$

substitute these values to get the roots

$x=\frac{1+\sqrt{1-4*1*-2} }{2} =2\\x=\frac{1-\sqrt{1-4*1*-2} }{2} =-1$

that is the values of x are real, unequal, and irrational