find the zero of the following quadratic polynomial 3x²-5x-2 and verify the relationship between the zeros and the cofficent
Answers
Let f(x) = 3x2 + 5x – 2
By splitting the middle term,
we get f(x) = 3x2 + (6 – 1)x – 2
[∵ 5 = 6 – 1 and 2×3 = 6]
= 3x2 + 6x – x – 2
= 3x(x + 2) – 1(x + 2)
= (3x – 1) (x + 2)
On putting f(x) = 0 ,
we get (3x – 1) (x + 2) = 0
⇒ 3x – 1 = 0 or x + 2 = 0
x = 1/3 or x = – 2
Thus, the zeroes of the given polynomial 3x2 + 5x – 2 are – 2 and 1/3.
Verification :
So, the relationship between the zeroes and the coefficients is verified .
Given :
- Quadratic polynomial 3x² - 5x - 2
To Find :
- Zeros of quadratic polynomial & verify the relationship between coefficients and the zeros.
According to the question,
⇒ 3x² - 5x - 2
⇒ 3x² - 6x + x - 2
⇒ 3x(x - 2) + 1(x - 2)
⇒ (3x + 1) (x - 2)
⇒ x = - 1/3 and 2
So,the zeros of the quadratic polynomial are - 1/3 and 2.
Now, we will verify the relationship between coefficients and zeros :-
★ Sum of zeros = -b/a
⇒ 2 + (- 1/3) = -(-5/3)
⇒ 2 - 1/3 = 5/3
⇒ 6 - 1/3 = 5/3
⇒ 5/3 = 5/3
★ Product of zeros = c/a
⇒ 2 × -1/3 = -2/3
⇒ -2/3 = -2/3
Hence,Verified.
________________________________