(b) If the parabola has the expression as p(x) = x² - 2x - 3 , then the zeroes of this polynomial are
Answers
Answer:
The zeroes of x² - 2x - 3 are 3 and -1
Step-by-step explanation:
The given Quadratic Expression is → x² - 2x - 3
To find the zeroes of this polynomial we factorize it by splitting the middle term.
For this; find 2 numbers such that:
- Their product = -3 and
- Their sum = -2
The 2 numbers which satisfy these 2 conditions are +1 and -3
x² - 2x - 3 = 0
⇒ x² + x - 3x - 3 = 0
⇒ x (x + 1) - 3 (x + 1) = 0
⇒ (x - 3) (x + 1) = 0
⇒ x = 3 or -1
∴ The 2 zeroes of this quadratic Polynomial = 3, -1
Alternative Method:
Here in this method plot the graph of the given quadratic polynomial. The places where the parabola touches the X-axis are its zeroes.
(Refer to the attachment for graph*)
From the graph, it can be clearly noted that the zeroes of the polynomial are 3 and -1
(*Graph attached here is made with Desmos Graph)
