Question

find the zeros of the given polynomial and verify the relationship between zeros and coefficients it 2x2-5x+3​

Answer 1

Answer:

2xsquare - 2x -3x +3

2x[x-1] -3[x-1]

[2x-3] [x-1]

2x=3

x=3/2

x=1 are the zeroes

sum = -b/a

LHS                                   RHS

3/2 + 1                                 -[-5]/2

5/2                                         5/2

product = c/a

LHS                                    RHS

3/2 *1                                      3/2

3/2

Step-by-step explanation:

Answer 2

Gɪᴠᴇɴ

Quadratic polynomial = 2x² - 5x + 3

Tᴏ ꜰɪɴᴅ

Zeros of polynomial & verify relationship b/w zeros & co-efficients.

Sᴏʟᴜᴛɪᴏɴ

Let the zeros of polynomial be a & ß

⇒ 2x² - 5x + 3 = 0

⇒ 2x² - 2x - 3x + 3 = 0

⇒ 2x(x - 1) -3(x - 1) = 0

⇒ (2x - 3)(x - 1) = 0

⇒ 2x = 3 or, x = 1

⇒ x = 3/2 or, x = 1

Tʜᴇʀᴇꜰᴏʀᴇ,

Zeros of polynomial are : 3/2 & 1 .

Now verifying relations b/w zeros & coefficients :

Relationship ❶ 

⇾ Sum of zeros = -coefficient of x/coefficient of x

⇾ 3/2 + 1 = -(-5)/2

⇾ (3 + 2)/2 = 5/2

⇾ 5/2 = 5/2 [Hᴇɴᴄᴇ Vᴇʀɪꜰɪᴇᴅ!]

Relationship ❷

⇾ Product of zeros = Constant term/Coefficient of x²

⇾ 3/2 × 1 = 3/2

⇾ 3/2 = 3/2 [Hᴇɴᴄᴇ Vᴇʀɪꜰɪᴇᴅ!]