Question

Draw the graph of the following quadratic equation and state their nature of solutions. : x^2+2x+5=0​

Answer 1

Step-by-step explanation:

Given :-

x²+2x+5 =0

To find :-

Draw the graph of the quadratic equation and state their nature of solutions ?

Solution :-

Drawing the graph :-

See the above attachment

Scale :- On X-axis 1 cm = 1 unit

On Y-axis 1 cm = 1 unit

Observations :-

• The graph of the given equation is an U -shaped curve called Parabola.

• The graph of the given equation does not touches the X-axis at any point .

• So ,It has no real roots .

Finding the nature of the roots :-

To find the nature of the roots we have to find its discriminant value.

Given quadratic equation is x²+2x+5 = 0

On Comparing this with the standard quadratic equation ax²+bx+c = 0

a = 1

b = 2

c = 5

We know that

Discriminant of ax²+bx+c = 0 is D = b²-4ac

=> D = 2²-4(1)(5)

=> D = 4-20

=> D = -16 < 0

Since , D<0 the equation has no real roots i.e they are imaginary roots.

Answer :-

The given equation has no real roots .

The nature of the roots is No real roots i.e imaginary roots.

Used formulae:-

• The standard quadratic equation is ax²+bx+c = 0

• Discriminant of ax²+bx+c = 0 is D = b²-4ac

• If D > 0 , it has two real and distinct roots.

• If D = 0 , it has equal and real roots.

• If D<0 the equation has no real roots i.e they are imaginary roots.

• The root is also called the Solution.

Answer 2

Answer:

Step-by-step explanation: