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3x² + 4x - 4. Find the zeroes of the polynomial, and verify the relation between the coefficients and the zeroes of the polynomial

Solution:

Given, the polynomial is 3x² + 4x - 4.

We have to find the relation between the coefficients and zeros of the polynomial

Let 3x² + 4x - 4 = 0

On factoring,

= 3x² + 6x - 2x - 4

= 3x(x + 2) - 2(x + 2)

= (3x - 2)(x + 2)

Now, 3x - 2 = 0

3x = 2

x = 2/3

Also, x + 2 = 0

x = -2

Therefore,the zeros of the polynomial are 2/3 and -2.

We know that, if 𝛼 and ꞵ are the zeroes of a polynomial ax² + bx + c, then

Sum of the roots is 𝛼 + ꞵ = -coefficient of x/coefficient of x² = -b/a

Product of the roots is 𝛼ꞵ = constant term/coefficient of x² = c/a

From the given polynomial,

coefficient of x = 4

Coefficient of x² = 3

Constant term = -4

Sum of the roots:

LHS: 𝛼 + ꞵ

= 2/3 - 2

= (2-6)/3

= -4/3

RHS: -coefficient of x/coefficient of x²

= -4/3

LHS = RHS

Product of the roots

LHS: 𝛼ꞵ

= (2/3)(-2)

= -4/3

RHS: constant term/coefficient of x²

= -4/3

LHS = RHS

✦ Try This: Find the zeroes of the polynomial 4x² + 3x - 3, and verify the relation between the coefficients and the zeroes of the polynomial

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2

NCERT Exemplar Class 10 Maths Exercise 2.3 Problem 2

3x² + 4x - 4. Find the zeroes of the polynomial, and verify the relation between the coefficients and the zeroes of the polynomial

Summary:

The zeroes of the polynomial 3x² + 4x - 4 are -2 and 2/3. The relation between the coefficients and zeros of the polynomial are : Sum of the roots = -b/a = -4/3 Product of the roots = c/a = -4/3.

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