Question

If a and b are the zeroes of the following polynomial then the value of ab is 2x2+5x-10

Answer 1

Answer:

if a and b are the zeroes of the polynomial 2x²+5x-10

then

a•b = -10/2

a•b = -5 Ans.

Answer 2

Answer :

ab = -5

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 a and b are the zeros of the quadratic polynomial Ax² + Bx + C , then ;

• Sum of zeros , (a + b) = -B/A

• Product of zeros , (ab) = C/A

★ If a and b are the zeros of a quadratic polynomial , then that quadratic polynomial is given as :

k•[ x² - (a + b)x + ab ] , 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 ;

2x² + 5x - 10

Comparing the given quadratic polynomial with the general quadratic polynomial Ax² + Bx + C , we have ;

A = 2

B = 5

C = -10

Also ,

It is given that , a and b are the zeros of the given quadratic polynomial .

Thus ,

=> Sum of zeros = -B/A

=> a + b = -5/2

Also ,

=> Product of zeros = C/A

=> a × b = -10/2

=> ab = -5

Hence ,

ab = -5