Question

29. Find the zeroes of the polynomial 4x + 4x – 3 and verity the relationship between
zeroes and the coefficients of polynomials.​

Answer 1

Answer:

Explanation:

Given :

• Quadratic polynomial, 4x² + 4x - 3 = 0.

To Find :

• The relationship between zeroes and the coefficient of polynomials.

Solution :

Given that, Quadratic polynomial, 4x² + 4x - 3 = 0.

On camping with, ax² + bx + c = 0 We get;

=> a = 4 , b = 4 , c = -3

We need to find zeroes of given quadratic polynomial,

4x² + 4x - 3 = 0

=> 4x² + 6x - 2x - 3 = 0

=> 2x(2x + 3) - 1(2x + 3) = 0

=> (2x + 3) (2x - 1) = 0

=> x = -3/2 & x = 1/2

=> α = -3/2 & β = 1/2

Now,

• Sum of zeroes ::

=> α + β = -b/a

=> -3/2 + 1/2 = -4/4

=> -3 + 1/2 = -1

=> -2/2 = -1

=> -1 = -1

• Product of zeroes ::

=> αβ = c/a

=> -3/2 × 1/2 = -3/4

=> -3 × 1/2 × 2 = -3/4

=> -3/4 = -3/4

• Hence, Relationship is verified!!

Answer 2

Answer:-

Given :-

• Quadratic polynomial, 4x² + 4x - 3 = 0.

To Find :-

• The relationship between zeroes and the coefficient of polynomials.

Solution :-

Given that, Quadratic polynomial, 4x² + 4x - 3 = 0.

On camping with, ax² + bx + c = 0 We get;

=> a = 4 , b = 4 , c = -3

We need to find zeroes of given quadratic polynomial,

4x² + 4x - 3 = 0

=> 4x² + 6x - 2x - 3 = 0

=> 2x(2x + 3) - 1(2x + 3) = 0

=> (2x + 3) (2x - 1) = 0

=> x = -3/2 & x = 1/2

=> α = -3/2 & β = 1/2

Now,

• Sum of zeroes ::

=> α + β = -b/a

=> -3/2 + 1/2 = -4/4

=> -3 + 1/2 = -1

=> -2/2 = -1

=> -1 = -1

• Product of zeroes ::

=> αβ = c/a

=> -3/2 × 1/2 = -3/4

=> -3 × 1/2 × 2 = -3/4

=> -3/4 = -3/4

Hence, Relationship is verified!!