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How many zeros does the polynomial (x – 3) 2 – 4 can have? Also, find its zeroes.

 How many zeros does the polynomial (x – 3)2 – 4 can have? Also, find its zeroes.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Given equation is (x – 3)^2– 4

Now, expand this equation.

=> x^2+ 9 – 6x – 4

= x^2– 6x + 5

As the equation has a degree of 2, the number of zeroes will be 2.

Now, solve x^2– 6x + 5 = 0 to get the roots.

So, x^2– x – 5x + 5 = 0

=> x(x – 1) -5(x – 1) = 0

=> (x – 1)(x – 5) = 0

x = 1, x = 5

So, the roots are 1 and 5.

Thanks

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