Question

Q.11 Find the zeros of quadratic polynomial.2x²-8+6

and verify the relation between zeros

and coefficients.​

Answer 1

Answer:

Given polynamial

f(x) = 2x2 – 8x + 6

= 2x2 – 6x – 2x + 6

= 2x(x – 3) – 2(x – 3)

= (x – 3) (2x – 2)

To find zeros of polynomial f(x), f(x) = 0.

⇒ f(x) = 0

⇒ (x – 3)(2x – 2) = 0

⇒ x – 3 = 0 or 2x – 2 = 0

⇒ x – 3 or x = 1

Zeros of polynomial 2x2 – 8x + 6 are 1 and 3.

Relation between zeros and coefficient:

Sum of zeros = 1 + 3 = 4

Product of zeros = 1 × 3 = 3

comparing polynomial by ax2 + bx + c = 0

a = 2, b = -8, c = 6

Sum of zeros = - b/a

= -(-8)/2

= 8/2 = 4

Product of zeros = c/a = 6/2 = 3

Thus there is a relationship between zeros and coefficient.