Question

If a and ß are the zeroes of the polynomial
2x² +5x+1, then the value of a+ß+a*ß​

Answer 1

Answer:

–2

Note:

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

Sum of zeros , (a+ß) = -B/A

Product of zeros , (a•ß) = C/A

Solution:

Here,

The given quadratic polynomial is ;

2x² + 5x + 1 .

Clearly ,

A = 2

B = 5

C = 1

Also,

It is given that , a and ß are the zeros of the given quadratic polynomial , thus ;

=> Sum of zeros = -B/A

=> a + ß = -5/2

Also,

=> Product of zeros = C/A

=> a•ß = 1/2

Now,.

a + ß + a•ß = -5/2 + 1/2

= (-5+1)/2

= -4/2

= -2

Hence,

The required value of a + ß + a•ß = -2