Question

verify the relationship between the co-efficient of the equation 3x^2-x-4​

Answer 1

ANSWER:

• Zeros are (-1) and 4/3

GIVEN:

• p(x) = 3x²-x-4

TO VERIFY:

• Relationship between zeros and co-efficient

SOLUTION:

• P(x) = 3x²-x-4

Firstly we have to find the roots of the given polynomial.

= 3x²-x-4

= 3x² -4x + 3x -4

= ( 3x² +3x) + (-4x-4)

= 3x(x+1) -4(x+1)

= (x+1)(3x-4)

Either ; (x+1) = 0

=> x = (-1)

Either ;. (3x-4) = 0

=> 3x= 4

=> x = 4/3

Sum of zeros :

$= - 1 + \frac{4}{3} \\ \implies \frac{ - ( - 1)}{3} \: \: \: \: \: = \frac{ - (coefficient \: of \: x)}{coefficient \: of \: x {}^{2} }$

Product of zeros

$= \frac{ - 1}{1} \times \frac{4}{3} \\ = \frac{ - 4}{3} \: \: \: \: \: = \frac{constant \: term}{coefficient \: of \: x {}^{2} }$

VERIFIED!!!

Answer 2

Answer:

Given:

We have been given a polynomial 3x^2-x-4.

To Verify:

We need to verify the relationship between the 3 coefficients of this equation.

Solution:

It is given that p(x) = 3x^2-x-4

Inorder to verify the relationship between coefficients, we should know the roots of this equation.

We can find its roots by splitting the middle term, we get

3x^2-x-4

=> 3x^2 - 4x + 3x - 4

=> (3x^2 + 3x) + (-4x-4)

=> 3x (x+1) -4(x+1)

=> (x+1) (3x-4)

Either (x + 1) = 0 or (3x - 4) =0.

x + 1 = 0

=> x = -1

3x - 4 = 0

=> 3x = 4

=> x = 4/3

Now, sum of zeroes = ( -1 + 4/3)

= (-3 + 4)/3

= 1/3 = -b/a

Product of zeroes = (-1 × 4/3)

= -4/3 = c/a

Hence verified!