Question

find the zero of the following quadratic polynomial 3x²-5x-2 and verify the relationship between the zeros and the cofficent​

Answer 1

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 .

Answer 2

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.

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