## Find the zeroes of the quadratic polynimial 3x²-x-4 and verify the relationship between the zeroes and the coefficien

Question

Find the zeroes of the quadratic polynimial 3x²-x-4 and verify the relationship between the zeroes and the coefficien

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7 months 2021-10-13T17:57:56+00:00 2 Answers 0 views 0

## Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros .

★ The general form of a quadratic polynomial is given as ; ax² + bx + c .

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

★ If α and ß are the zeros of a quadratic polynomial , then that quadratic polynomial is given as : k•[ x² – (α + ß)x + αß ] , k ≠ 0.

★ The discriminant , D of the quadratic polynomial ax² + bx + c is given by ;

D = b² – 4ac

★ If D = 0 , then the zeros are real and equal .

★ If D > 0 , then the zeros are real and distinct .

★ If D < 0 , then the zeros are unreal (imaginary) .

## Solution :

Here ,

The given quadratic polynomial is ;

3x² – x – 4 .

Clearly ,

a = 3

b = -1

c = -4

For finding zeros of the given quadratic polynomial , equate it to zero .

Thus ,

=> 3x² – x – 4 = 0

=> 3x² – 4x + 3x – 4 = 0

=> x(3x – 4) + (3x – 4) = 0

=> (3x – 4)(x + 1) = 0

=> x = 4/3 , -1

Now ,

• Sum of zeros = 4/3 + (-1)

= 4/3 – 1

= (4 – 3)/3

= 1/3

• -b/a = -(-1)/3 = 1/3

Clearly , Sum of zeros = -b/a

Also ,

• Product of zeros = (4/3)×(-1) = -4/3

• c/a = -4/3

Clearly , Product of zeros = c/a

## Hence verified .

Step-by-step explanation:

3x^2-x-4=0

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

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

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

3x-4=0

x=4/3

x+1=0

x=-1

The sum of the zeroes of given polynomial=-b/a

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

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

1/3=1/3

Product of the zeroes of given polynomial=c/a

-1×4/3=-4/3

-4/3=-4/3