Question

Draw the graph of the following quadratic equation and state their nature of solutions. :x^2-8x+16=0​

Answer 1

Step-by-step explanation:

Given :-

x²-8x+16 = 0

To find :-

Draw the graph of the following quadratic equation and state their nature of solutions.

x²-8x+16=0

Solution :-

Given Quadratic equation is x²-8x+16 = 0

Finding the graph :-

Let y = x²-8x+16

On putting 1,2,3,... values of x in the function

We get points (0,16),(1,9),(2,4),(3,1),(4,0),(-1,25),...

Scale :-

On X-axis 1 cm = 1 unit

On Y-axis 1 cm = 2 units

Observations :

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

2. The graph cuts the X-axis at (4,0).

3. Roots of the given equation are 4 and 4

Result :-

Solution of the given equation x²-8x+16 = 0 is (4,4)

Finding the nature of the roots:-

Given equation is x²-8x+16 =0

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

a = 1

b=-8

c = 16

The discriminant of the equation ax²+bx+c = 0 is D=b²-4ac

D = (-8)²-4(1)(16)

=> D = 64-64

=> D = 0

Since D = 0 ,the equation has two real and equal roots.

Check:-

x²-8x+16 = 0

=> x²-4x-4x+16 = 0

=> x(x-4)-4(x-4) = 0

=> (x-4)(x-4) = 0

=>x-4 = 0 or x-4 = 0

=> x = 4 and x=4

Verified the given relations in the given problem.

Answer:-

Roots of the given equation are 4 and 4

Nature of the roots : x²-8x+16=0 has two real and equal roots.

Used formulae:-

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

• The quadratic equation has at most two roots

• The discriminant of ax²+bx+c = 0 is D=b2²-4ac

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

• If D<0 ,then it has no real roots i.e.imaginary.

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