How many zeroes does the polynomial (x-3)2-4 can have ? Also find its zeroes
Answers
Answer:
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Step-by-step explanation:
Since, it is a quadratic polynomial it will have two zeroes. Lets find the zeroes by quadratic equation. Hence,the zeroes of the polynomial is 5 and 1.
x=5
Step-by-step explanation:
(x-3)2-4=0
2x-6-4=0
As it is a linear equation it has 1 zero
2x-10=0
2x=10
x=10/2=5
x=5
Answer:
the two roots of the quadratic equation (x - 3)² - 4 are 1 and 5.
Step-by-step explanation:
Given,
The expression (x - 3)² - 4
To find,
Number of zeroes of the polynomial (x - 3)² - 4 and its zeroes
Calculation,
(x - 3)² - 4
= (x² - 6x + 9) - 4 (since, (a - b)² = a² - 2ab + b²)
= x² - 6x + 5....(1)
Since equation (1) is a quadratic equation. Hence it has two roots.
Now for finding the roots of the quadratic equation x² - 6x + 5, we need to equate the quadratic equation to zero.
i.e. x² - 6x + 5 = 0
x² - 5x - x + 5 = 0
⇒ x(x - 5) -1(x - 5) - 0
⇒ (x - 5)(x - 1) = 0
i.e. x = 1 or 5
Therefore, the two roots of the quadratic equation (x - 3)² - 4 are 1 and 5.
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