Q. 1 F5.0( 1 Vote )

Find the zeros of

Answer :

Let f(x) = 3x2 – 5x + 2.

To find out zeros of the given polynomial.


We put f(x) = 0


3x2 – 5x + 2 = 0


To find out roots of this polynomial we use splitting of middle term method.


According to this method we need to find two numbers whose sum is – 5 and product is 6.


3x2 – (3 + 2)x + 2 = 0


3x2 – 3x – 2x + 2 = 0


3x(x – 1) – 2(x – 1) = 0


(3x – 2)(x – 1) = 0


When, 3x – 2 = 0


Then, x = .


Again when, x – 1 = 0


then, x = 1


Our zeros are α = and β = 1.


sum of zeros = α + β = + 1


sum of zeros = α + β =


Product of zeros = αβ = .


Now, Comparing f(x) = 3x2 – 5x + 2 with standard equation ax2 + bx + c.


We get, a = 3, b = – 5 and c = 2.


We can verify,


Sum of zeros =


i.e. α + β =


α + β =


Product of zeros =


αβ =


Hence, relationship between zeros and coefficient is verified.


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