Draw the graph of the polynomial x^-4x-5 find the zeroes and justify your answer.
Answers
EXPLANATION.
Graph of the equation.
⇒ x² - 4x - 5 = 0.
As we know that,
⇒ y = x² - 4x - 5 = 0.
Factorizes the equation into middle term splits, we get.
⇒ y = x² - 5x + x - 5 = 0.
⇒ y = x(x - 5) + 1(x - 5) = 0.
⇒ y = (x + 1)(x - 5) = 0.
Zeroes of the equation, we get.
⇒ x = - 1 and x = 5.
Put the value of x = -1 in equation, we get.
⇒ y = (-1)² - 4(-1) - 5.
⇒ y = 1 + 4 - 5.
⇒ y = 5 - 5.
⇒ y = 0.
Their Co-ordinates = (-1,0).
Put the value of x = 5 in equation, we get.
⇒ y = (5)² - 4(5) - 5.
⇒ y = 25 - 20 - 5.
⇒ y = 25 - 25.
⇒ y = 0.
Their Co-ordinates = (5,0).
Put the values of x = 0 in equation, we get.
⇒ y = (0)² - 4(0) - 5.
⇒ y = -5.
Their Co-ordinates = (0,-5).
EXPLANATION.
Graph of the equation.
⇒ x² - 4x - 5 = 0.
As we know that,
⇒ y = x² - 4x - 5 = 0.
Factorizes the equation into middle term splits, we get.
⇒ y = x² - 5x + x - 5 = 0.
⇒ y = x(x - 5) + 1(x - 5) = 0.
⇒ y = (x + 1)(x - 5) = 0.
Zeroes of the equation, we get.
⇒ x = - 1 and x = 5.
Put the value of x = -1 in equation, we get.
⇒ y = (-1)² - 4(-1) - 5.
⇒ y = 1 + 4 - 5.
⇒ y = 5 - 5.
⇒ y = 0.
Their Co-ordinates = (-1,0).
Put the value of x = 5 in equation, we get.
⇒ y = (5)² - 4(5) - 5.
⇒ y = 25 - 20 - 5.
⇒ y = 25 - 25.
⇒ y = 0.
Their Co-ordinates = (5,0).
Put the values of x = 0 in equation, we get.
⇒ y = (0)² - 4(0) - 5.
⇒ y = -5.
Their Co-ordinates = (0,-5).