Question

Find the relation b/w zeroes and coefficients of 4x^2-4x+1.

Answer 1

Answer :

• Sum of zeros = 1

• Product of zeros = 1/4

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 ;

4x² - 4x + 1 .

Comparing the given quadratic polynomial with the general quadratic polynomial ,

We have ;

a = 4

b = -4

c = 1

Thus ,

Sum of zeros = -b/a = -(-4)/4 = 1

Also ,

Product of zeros = c/a = 1/4

Hence ,

• Sum of zeros = 1

• Product of zeros = 1/4