Question

Find the zeroes of the polynomial 3x²-x-4 and verify the
relationship between Zeroes and co-efficients.​

Answer 1

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Answer 2

Explanation:

Given:-

Polynomial 3x^2-x-4

To find:-

Find the zeroes of the polynomial 3x^2-x-4 and verify the relationship between Zeroes and co-efficients ?

Solution:-

Given quardratic polynomial is 3x^2-x-4

To get the zeores we write it as

=> 3x^2-x-4 = 0

=> 3x^2 +3x -4x -4 = 0

=> 3x(x+1)-4(x+1) = 0

=>(x+1)(3x-4) = 0

=>x+1 = 0 or 3x-4 = 0

=> x= -1 or 3x = 4

=>x= -1 or x = 4/3

The zeores of the given Polynomial are -1 and 4/3

Relationship between the zeroes and the coefficients:-

Let P(x) = 3x^2-x-4

on Comparing this with the standard quadratic Polynomial ax^2+bx+c

a = 3

b= -1

c=-4

Let α = -1 and β = 4/3

i) Sum of the zeroes

=> α+β

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

=> (-3+4)/3

=> 1/3

=> -(-1/3)

=> -(Coefficient of x)/Coefficient of x^2

=> -b/a

α + β = -b/a

ii) Product of the zeroes

=>αβ

=> (-1)×(4/3)

=> -4/3

=> Constant term / Coefficient of x^2

=> c/a

αβ = c/a

Verified the relationship between the zeroes and the coefficients of the given polynomial 3x^2-x-4

Answer:-

Zeroes of the given quardratic polynomial are -1 and 4/3

Used formulae:-

• The standard quadratic Polynomial is ax^2+bx+c

• Sum of the zeroes α+ β = -b/a

• Product of the zeroes αβ = c/a