Graph the quadratic equation x²-8x +16= 0 and
State the nature of their solution
Answers
Answer:
x²-8x+16=0
x²-4x-4x+16=0
x(x-4) -4(x-4)=0
(x-4) (x-4)= 0
x=4 and x=4
Given:
A Quadratic equation x²-8x +16= 0.
To Find:
The nature and the solutions of the quadratic equations.
Solution:
The given problem can be solved using the concepts of Quadratic equations.
1. The given equation is x²-8x +16= 0.
2. The roots of the given solution can be calculated as,
=> x²-8x +16= 0,
=> x²-4x - 4x +16= 0,
=>x(x-4) -4(x-4) = 0,
=> (x-4)(x-4) = 0,
=> x = 4,4 are the roots of the given eqaution.
3. Both the roots of the given equation are the same and the values are real.
4. Consider a quadratic equation ax²+bx +c = 0(a>0) having equal roots as (c,c) the graph of the quadratic equation is a parabola touching the x-axis at one point.
5. The given Quadratic equation is the same case mentioned above, hence its graph will be a parabola facing towards the positive y-axis which is touching the x-axis at one point.
Therefore, the quadratic equation x²-8x +16= 0 has equal roots (4,4) and the graph of the equation is a parabola touching the x-axis at one point, facing towards the positive y-axis.