Find the zeroes of the following quadratic polynomial and varify the r

1.	Find the zeroes of the following quadratic polynomial and varify the relentonship between the zeroes and the corfficent : f(x)=6x^-3-7x
Answer» AnswEr:- ZEROS of polynomial = -1/3 & 3/2 $\rule{200}{1}$ Here, given polynomial is : ☛ f(x) = 6x² - 3 - 7x = 0 We can find zeros of polynomial by factorization method:- ⇒ 6x² - 3 - 7x = 0 ⇒ 6x² - 7x - 3 = 0 ⇒ 6x² - 9x + 2x - 3 = 0 ⇒ 3x(2x - 3) + 1(2x - 3) = 0 ⇒ (3x + 1)(2x - 3) = 0 ⇒ 3x = -1 or 2x = 3 ⇒ x = -1/3 or x = 3/2 Therefore, $\therefore\underline{\textsf{Zeros of polynomial = {\textbf{-1/3 \& 3/2 }}}}$ $\rule{200}{1}$ Verification:- Here, α = -1/3 β = 3/2 And, Coefficient of x²(a) = 6 Coefficient of x(b) = -7 Constant term(c) = -3 Relationship 1:- ☛ Sum of zeros = -b/a ⇒ -1/3 + 3/2 = -(-7)/6 ⇒ (-2 + 9)/6 = 7/6 ⇒ 7/6 = 7/6 [HENCE VERIFIED!] Relationship 2:- ☛ PRODUCT of zeros = c/a ⇒ -1/3 × 3/2 = -3/6 ⇒ -1/2 = -1/2 [Hence verified!] Therefore, Relation between the zeros and COEFFICIENTS are verified!

Find the zeroes of the following quadratic polynomial and varify the relentonship between the zeroes and the corfficent : f(x)=6x^-3-7x

Answer»

ZEROS of polynomial = -1/3 & 3/2

$\rule{200}{1}$

Here, given polynomial is :

☛ f(x) = 6x² - 3 - 7x = 0

We can find zeros of polynomial by factorization method:-

⇒ 6x² - 3 - 7x = 0

⇒ 6x² - 7x - 3 = 0

⇒ 6x² - 9x + 2x - 3 = 0

⇒ 3x(2x - 3) + 1(2x - 3) = 0

⇒ (3x + 1)(2x - 3) = 0

⇒ 3x = -1 or 2x = 3

⇒ x = -1/3 or x = 3/2

Therefore,

$\therefore\underline{\textsf{Zeros of polynomial = {\textbf{-1/3 \& 3/2 }}}}$

$\rule{200}{1}$

Verification:-

Here,

And,

Relationship 1:-

☛ Sum of zeros = -b/a

⇒ -1/3 + 3/2 = -(-7)/6

⇒ (-2 + 9)/6 = 7/6

⇒ 7/6 = 7/6 [HENCE VERIFIED!]

Relationship 2:-

☛ PRODUCT of zeros = c/a

⇒ -1/3 × 3/2 = -3/6

⇒ -1/2 = -1/2 [Hence verified!]

Therefore,

Relation between the zeros and COEFFICIENTS are verified!